{
"cells": [
{
"cell_type": "markdown",
"id": "a7626f43-b1e4-4427-a55c-0ba5a54cc575",
"metadata": {
"id": "a7626f43-b1e4-4427-a55c-0ba5a54cc575"
},
"source": [
"## Computational\n",
"\n",
"The solutions to problems in this section should be in the form of code. You might be required to state your observations, in which case, an empty markdown cell will be provided."
]
},
{
"cell_type": "markdown",
"id": "23eb3fe1-26c3-4590-a7a1-719306f0522d",
"metadata": {
"id": "23eb3fe1-26c3-4590-a7a1-719306f0522d"
},
"source": [
"## Problem 1 - Streaming Startup [15 points]\n",
"\n",
"This problem requires you to perform Bayesian updates for a simple problem.\n",
"\n",
"You wish to kick-start a company that would combine the best shows from Netflix and Prime Video on 1 platform. Two dataframes are created below to show the show title and the rating from 0 to 5 from Netflix and Prime Video."
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6502e84c-508e-4fe9-9fd1-e227e927ac7a",
"metadata": {
"id": "6502e84c-508e-4fe9-9fd1-e227e927ac7a"
},
"outputs": [],
"source": [
"import pandas as pd\n",
"import numpy as np\n",
"from scipy.stats import randint\n",
"import matplotlib.pyplot as plt"
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "78a5ffa7-2980-42f5-9b76-613f2202877c",
"metadata": {
"id": "78a5ffa7-2980-42f5-9b76-613f2202877c"
},
"outputs": [],
"source": [
"# data for netflix\n",
"net_data = {\n",
" 'name': ['Seinfeld', 'Better Call Saul', 'Breaking Bad', 'The Queens Gambit', 'Bojack Horseman', 'Attack on Titan', 'Cyberpunk', 'Space Force', 'One Punch Man', 'Flash',\n",
" 'Sex Education', 'Inside Job', 'Love Death Plus Robots', 'Wednesday', 'Lucifer', 'Money Heist', 'Lupin', 'Stranger Things', 'Lock and Key', 'The Witcher', 'Dark'],\n",
" 'rating': [3.5, 4.5, 4.5, 3.75, 4, 4.5, 4.5, 3, 4, 3.5,\n",
" 3, 4.5, 4.9, 4.5, 4.6, 3.8, 2.5, 4, 2.6, 4.2, 4.3]\n",
"}\n",
"\n",
"prime_data = {\n",
" 'name':['The Boys', 'Fleabag', 'Spongebob Squarepants', 'Suits', 'Vikings'],\n",
" 'rating':[4.5, 5, 4.7, 3.5, 4.2]\n",
"}\n",
"\n",
"# Creating dataframes for Netflix and Prime Video\n",
"netflix = pd.DataFrame(net_data)\n",
"prime = pd.DataFrame(prime_data)"
]
},
{
"cell_type": "code",
"source": [
"netflix.head()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 206
},
"id": "IZorzxUHIcCp",
"outputId": "2bfa71ae-b9b3-4163-b809-c96aa7ca0394"
},
"id": "IZorzxUHIcCp",
"execution_count": 3,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" name rating\n",
"0 Seinfeld 3.50\n",
"1 Better Call Saul 4.50\n",
"2 Breaking Bad 4.50\n",
"3 The Queens Gambit 3.75\n",
"4 Bojack Horseman 4.00"
],
"text/html": [
"\n",
" <div id=\"df-ecec55b2-cad4-4767-b1ee-db9b172817fa\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>name</th>\n",
" <th>rating</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>Seinfeld</td>\n",
" <td>3.50</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Better Call Saul</td>\n",
" <td>4.50</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Breaking Bad</td>\n",
" <td>4.50</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>The Queens Gambit</td>\n",
" <td>3.75</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>Bojack Horseman</td>\n",
" <td>4.00</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-ecec55b2-cad4-4767-b1ee-db9b172817fa')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-ecec55b2-cad4-4767-b1ee-db9b172817fa button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-ecec55b2-cad4-4767-b1ee-db9b172817fa');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-b244dd3a-4ac8-484b-a6ba-e01c64ec982a\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-b244dd3a-4ac8-484b-a6ba-e01c64ec982a')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-b244dd3a-4ac8-484b-a6ba-e01c64ec982a button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 3
}
]
},
{
"cell_type": "code",
"source": [
"prime.head()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 206
},
"id": "50VrGm_BIe3F",
"outputId": "cf562eff-4b0b-4eb0-a247-1645bdd9b847"
},
"id": "50VrGm_BIe3F",
"execution_count": 4,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" name rating\n",
"0 The Boys 4.5\n",
"1 Fleabag 5.0\n",
"2 Spongebob Squarepants 4.7\n",
"3 Suits 3.5\n",
"4 Vikings 4.2"
],
"text/html": [
"\n",
" <div id=\"df-64840d53-1cb4-4388-a6e9-6777e227253f\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>name</th>\n",
" <th>rating</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>The Boys</td>\n",
" <td>4.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>Fleabag</td>\n",
" <td>5.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>Spongebob Squarepants</td>\n",
" <td>4.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>Suits</td>\n",
" <td>3.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>Vikings</td>\n",
" <td>4.2</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-64840d53-1cb4-4388-a6e9-6777e227253f')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-64840d53-1cb4-4388-a6e9-6777e227253f button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-64840d53-1cb4-4388-a6e9-6777e227253f');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-e7ff6743-dffe-48c0-924a-fdace3b0912d\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-e7ff6743-dffe-48c0-924a-fdace3b0912d')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-e7ff6743-dffe-48c0-924a-fdace3b0912d button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 4
}
]
},
{
"cell_type": "markdown",
"id": "4469f4f8-a85c-469e-8a23-46e053ad23d0",
"metadata": {
"id": "4469f4f8-a85c-469e-8a23-46e053ad23d0"
},
"source": [
"Your product is now in it's testing stage, and a volunteer selects a TV show at random to watch. He was supposed to record the name of the platform and the rating of the show, but forgot to record it. Thankfully he remembers that the rating of the show was at least 4. Find out the probability of the show being from Netflix.\n",
"\n",
"**Here is a Bayes table with the priors to get you started:**"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "47c6f671-db01-4ddb-b302-feaed3078244",
"metadata": {
"id": "47c6f671-db01-4ddb-b302-feaed3078244"
},
"outputs": [],
"source": [
"table = pd.DataFrame(index=['Netflix', 'Prime'])\n",
"table['prior'] = randint(1, 3).pmf(np.arange(1,3))"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "437476cb-226c-42ed-afc8-547b1eac64c6",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 112
},
"id": "437476cb-226c-42ed-afc8-547b1eac64c6",
"outputId": "d6a9d312-067a-4106-cb92-f2de5b55edc8"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" prior\n",
"Netflix 0.5\n",
"Prime 0.5"
],
"text/html": [
"\n",
" <div id=\"df-8ef654fa-0ec1-434d-a036-b8105cabbf09\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prior</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Netflix</th>\n",
" <td>0.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Prime</th>\n",
" <td>0.5</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-8ef654fa-0ec1-434d-a036-b8105cabbf09')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-8ef654fa-0ec1-434d-a036-b8105cabbf09 button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-8ef654fa-0ec1-434d-a036-b8105cabbf09');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-d214b171-9340-4a98-b99c-8ef72d2fdb86\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-d214b171-9340-4a98-b99c-8ef72d2fdb86')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-d214b171-9340-4a98-b99c-8ef72d2fdb86 button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 6
}
],
"source": [
"table"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "7161a48f-9ba0-47f0-8c7a-d0bfbd93bdc7",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 112
},
"id": "7161a48f-9ba0-47f0-8c7a-d0bfbd93bdc7",
"outputId": "0cbd96bc-8a93-4ddd-e723-5e5bcf7a0400"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" prior probs\n",
"Netflix 0.5 0.5\n",
"Prime 0.5 0.5"
],
"text/html": [
"\n",
" <div id=\"df-f77749a6-d57e-4e51-927c-26118b6e16b4\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prior</th>\n",
" <th>probs</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Netflix</th>\n",
" <td>0.5</td>\n",
" <td>0.5</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Prime</th>\n",
" <td>0.5</td>\n",
" <td>0.5</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-f77749a6-d57e-4e51-927c-26118b6e16b4')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-f77749a6-d57e-4e51-927c-26118b6e16b4 button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-f77749a6-d57e-4e51-927c-26118b6e16b4');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-0d73c36b-43a5-4e02-9e62-0e7377176330\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-0d73c36b-43a5-4e02-9e62-0e7377176330')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-0d73c36b-43a5-4e02-9e62-0e7377176330 button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 7
}
],
"source": [
"# don't change prior, update probs\n",
"table['probs'] = table['prior']\n",
"table"
]
},
{
"cell_type": "markdown",
"id": "abfd11d1-d4ad-4bad-b648-41b633049276",
"metadata": {
"id": "abfd11d1-d4ad-4bad-b648-41b633049276"
},
"source": [
"**1.1 Define an update function to update table['probs'] based on the likelihood. [5 points]**"
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "ee169ff9-676f-43bc-8f01-45a90634702d",
"metadata": {
"id": "ee169ff9-676f-43bc-8f01-45a90634702d"
},
"outputs": [],
"source": [
"def update(table, likelihood):\n",
" '''\n",
" params:\n",
" table: table to be passed\n",
" table['probs']: column to be updated\n",
" likelihood: likelihood of the data\n",
" '''\n",
"\n",
" # Multiply the 'probs' column of the table with the likelihood\n",
" table['probs'] = table['probs'] * likelihood\n",
"\n",
" # Sum the values of the 'probs' column and store it in the 'data' variable\n",
" data = table['probs'].sum()\n",
"\n",
" # Divide the 'probs' column of the table by the value of 'data' to normalize the probabilities\n",
" table['probs'] = table['probs'] / data\n",
"\n",
" # Return the updated table\n",
" return table"
]
},
{
"cell_type": "markdown",
"id": "b991c1e1-dc8c-4c4e-80c2-7b461bfe31dd",
"metadata": {
"id": "b991c1e1-dc8c-4c4e-80c2-7b461bfe31dd"
},
"source": [
"**1.2 Calculate the likelihood for Netflix and Prime. [5 points]**"
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "7bf9077c-5366-45cb-848f-755b900695a8",
"metadata": {
"id": "7bf9077c-5366-45cb-848f-755b900695a8"
},
"outputs": [],
"source": [
"# Calculating the likelihood for Netflix\n",
"\n",
"# Count the number of movies in Netflix with rating >= 4 and store it in 'net_fav'\n",
"net_fav = len(netflix[netflix['rating'] >= 4])\n",
"\n",
"# Count the total number of movies in Netflix and store it in 'net_total'\n",
"net_total = len(netflix)\n",
"\n",
"# Calculate the likelihood for Netflix movies to have a rating >= 4 and store it in 'net_likelihood'\n",
"net_likelihood = net_fav / net_total\n",
"\n",
"# Calculating the likelihood for Prime\n",
"\n",
"# Count the number of movies in Prime with rating >= 4 and store it in 'prime_fav'\n",
"prime_fav = len(prime[prime['rating'] >= 4])\n",
"\n",
"# Count the total number of movies in Prime and store it in 'prime_total'\n",
"prime_total = len(prime)\n",
"\n",
"# Calculate the likelihood for Prime movies to have a rating >= 4 and store it in 'prime_likelihood'\n",
"prime_likelihood = prime_fav / prime_total\n",
"\n",
"# Store the likelihood values for Netflix and Prime in the 'likelihood' tuple\n",
"likelihood = (net_likelihood, prime_likelihood)"
]
},
{
"cell_type": "markdown",
"id": "30b5f882-89bc-4b8a-8bbe-9a6b6e9ec6f3",
"metadata": {
"id": "30b5f882-89bc-4b8a-8bbe-9a6b6e9ec6f3"
},
"source": [
"**1.3 Call the update function to update your belief. [2 points].**"
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "68a2197c-b6da-49a3-ae97-c6376c1b1b75",
"metadata": {
"id": "68a2197c-b6da-49a3-ae97-c6376c1b1b75"
},
"outputs": [],
"source": [
"# Call the update function to update the belief\n",
"table = update(table, likelihood)"
]
},
{
"cell_type": "code",
"source": [
"# The updated probabilities are copied and stored under 'prob1' for visualizing later\n",
"table['prob1'] = table['probs']\n",
"\n",
"# Inspect the updated table\n",
"table"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 112
},
"id": "IqO2JM9gS_qp",
"outputId": "59837ef4-a67e-4a56-fbb4-d7305a93921a"
},
"id": "IqO2JM9gS_qp",
"execution_count": 11,
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" prior probs prob1\n",
"Netflix 0.5 0.436242 0.436242\n",
"Prime 0.5 0.563758 0.563758"
],
"text/html": [
"\n",
" <div id=\"df-2442d991-3661-4b5d-bfba-e4eee22c7615\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prior</th>\n",
" <th>probs</th>\n",
" <th>prob1</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Netflix</th>\n",
" <td>0.5</td>\n",
" <td>0.436242</td>\n",
" <td>0.436242</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Prime</th>\n",
" <td>0.5</td>\n",
" <td>0.563758</td>\n",
" <td>0.563758</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-2442d991-3661-4b5d-bfba-e4eee22c7615')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-2442d991-3661-4b5d-bfba-e4eee22c7615 button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-2442d991-3661-4b5d-bfba-e4eee22c7615');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-24a87c65-0502-473e-96b9-d350ca908fff\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-24a87c65-0502-473e-96b9-d350ca908fff')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-24a87c65-0502-473e-96b9-d350ca908fff button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 11
}
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "8fc98b17-884c-4daf-afee-cec5ec9dc844",
"metadata": {
"id": "8fc98b17-884c-4daf-afee-cec5ec9dc844"
},
"outputs": [],
"source": [
"# DO NOT CHANGE THIS CELL\n",
"# updated probs copied and stored under prob1 for visualizing later\n",
"table['prob1'] = table['probs']"
]
},
{
"cell_type": "markdown",
"id": "8373ff38-b78a-4da7-9275-fd04d130413d",
"metadata": {
"id": "8373ff38-b78a-4da7-9275-fd04d130413d"
},
"source": [
"**1.4 Now he is watching another show. Note that the first show he watched will still be available on the platform (as if he has put the show\n",
"back on the platform). It again has at least a 4 point rating. What is the probability that it is from Netflix? [3 points]**"
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "f3a29b84-5471-4d14-83b8-9908743932d2",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 112
},
"id": "f3a29b84-5471-4d14-83b8-9908743932d2",
"outputId": "1ab1df73-2e99-4014-c667-318c6f6b8195"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" prior probs prob1\n",
"Netflix 0.5 0.374524 0.436242\n",
"Prime 0.5 0.625476 0.563758"
],
"text/html": [
"\n",
" <div id=\"df-1b0fae0e-fc2a-4161-a884-b8d7235316c6\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>prior</th>\n",
" <th>probs</th>\n",
" <th>prob1</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>Netflix</th>\n",
" <td>0.5</td>\n",
" <td>0.374524</td>\n",
" <td>0.436242</td>\n",
" </tr>\n",
" <tr>\n",
" <th>Prime</th>\n",
" <td>0.5</td>\n",
" <td>0.625476</td>\n",
" <td>0.563758</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-1b0fae0e-fc2a-4161-a884-b8d7235316c6')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-1b0fae0e-fc2a-4161-a884-b8d7235316c6 button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-1b0fae0e-fc2a-4161-a884-b8d7235316c6');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-43277e01-09a5-4e1a-b903-7873f79e614a\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-43277e01-09a5-4e1a-b903-7873f79e614a')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-43277e01-09a5-4e1a-b903-7873f79e614a button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 13
}
],
"source": [
"# Call the update function again to update the belief based on the new show being watched\n",
"table = update(table, likelihood)\n",
"\n",
"# To inspect the updated table\n",
"table"
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "260076c3-9432-4c1e-98d7-e2868ac5bfce",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 452
},
"id": "260076c3-9432-4c1e-98d7-e2868ac5bfce",
"outputId": "596e24d8-df24-4975-81c1-7d71ce54b627"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {}
}
],
"source": [
"# Visualizations\n",
"# DO NOT CHANGE THE CODE BELOW\n",
"\n",
"# Rearranging columns for visualization\n",
"table = table[['prior', 'prob1', 'probs']]\n",
"\n",
"# Finding the transpose of the table to aid plotting\n",
"net_print = table.T['Netflix']\n",
"prime_print = table.T['Prime']\n",
"fig, ax = plt.subplots()\n",
"ax.plot(net_print, '-o', label='Netflix', color='blue')\n",
"ax.plot(prime_print, '-o', label='Prime Video', color='green')\n",
"ax.set_title('Change in Prior, Prob1, and Probs')\n",
"ax.set_xticks([0, 1, 2])\n",
"ax.set_xticklabels(['Prior', 'Prob1', 'Probs'])\n",
"ax.legend()\n",
"ax.grid(True)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "e3dda9d0-a389-41c2-8b82-6c904872eb38",
"metadata": {
"id": "e3dda9d0-a389-41c2-8b82-6c904872eb38"
},
"source": [
"### Problem 2 - The League [60 points]"
]
},
{
"cell_type": "markdown",
"id": "f590744a-0cd2-4096-bb7e-86266cf16cba",
"metadata": {
"id": "f590744a-0cd2-4096-bb7e-86266cf16cba"
},
"source": [
"In this football problem, you will work like a data scientist and fill this end-to-end project to answer a question based on real data.\n",
"\n",
"On March 5 2023, Liverpool won a match against Manchester United by 7-0.\n",
"\n",
"In this problem, we will work on how confident should we be that Liverpool is a better team than Manchester United?"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "241e22db-96f4-470d-82d9-597b2892680a",
"metadata": {
"id": "241e22db-96f4-470d-82d9-597b2892680a"
},
"outputs": [],
"source": [
"# Import the pandas library as 'pd'\n",
"import pandas as pd\n",
"\n",
"# Import the 'poisson' and 'gamma' functions from 'scipy.stats'\n",
"from scipy.stats import poisson\n",
"from scipy.stats import gamma\n",
"\n",
"# Import the numpy library as 'np'\n",
"import numpy as np\n",
"\n",
"# Import the 'pyplot' module from 'matplotlib' as 'plt'\n",
"from matplotlib import pyplot as plt\n"
]
},
{
"cell_type": "code",
"source": [
"# Import necessary library for file upload\n",
"from google.colab import files\n",
"\n",
"def upload_file():\n",
" uploaded = files.upload()\n",
" for filename in uploaded.keys():\n",
" print('User uploaded file \"{name}\" with length {length} bytes'.format(\n",
" name=filename, length=len(uploaded[filename])))\n",
" return filename\n",
"\n",
"# Use the function to upload the file and read it into a dataframe\n",
"file_name = upload_file()"
],
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 95
},
"id": "Pii3efSjMw5e",
"outputId": "4c4953ff-061a-4b3c-d56c-19d1432f150d"
},
"id": "Pii3efSjMw5e",
"execution_count": 16,
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<IPython.core.display.HTML object>"
],
"text/html": [
"\n",
" <input type=\"file\" id=\"files-dfb3a959-0eca-4ada-936a-8d11a6a6f4b0\" name=\"files[]\" multiple disabled\n",
" style=\"border:none\" />\n",
" <output id=\"result-dfb3a959-0eca-4ada-936a-8d11a6a6f4b0\">\n",
" Upload widget is only available when the cell has been executed in the\n",
" current browser session. Please rerun this cell to enable.\n",
" </output>\n",
" <script>// Copyright 2017 Google LLC\n",
"//\n",
"// Licensed under the Apache License, Version 2.0 (the \"License\");\n",
"// you may not use this file except in compliance with the License.\n",
"// You may obtain a copy of the License at\n",
"//\n",
"// http://www.apache.org/licenses/LICENSE-2.0\n",
"//\n",
"// Unless required by applicable law or agreed to in writing, software\n",
"// distributed under the License is distributed on an \"AS IS\" BASIS,\n",
"// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.\n",
"// See the License for the specific language governing permissions and\n",
"// limitations under the License.\n",
"\n",
"/**\n",
" * @fileoverview Helpers for google.colab Python module.\n",
" */\n",
"(function(scope) {\n",
"function span(text, styleAttributes = {}) {\n",
" const element = document.createElement('span');\n",
" element.textContent = text;\n",
" for (const key of Object.keys(styleAttributes)) {\n",
" element.style[key] = styleAttributes[key];\n",
" }\n",
" return element;\n",
"}\n",
"\n",
"// Max number of bytes which will be uploaded at a time.\n",
"const MAX_PAYLOAD_SIZE = 100 * 1024;\n",
"\n",
"function _uploadFiles(inputId, outputId) {\n",
" const steps = uploadFilesStep(inputId, outputId);\n",
" const outputElement = document.getElementById(outputId);\n",
" // Cache steps on the outputElement to make it available for the next call\n",
" // to uploadFilesContinue from Python.\n",
" outputElement.steps = steps;\n",
"\n",
" return _uploadFilesContinue(outputId);\n",
"}\n",
"\n",
"// This is roughly an async generator (not supported in the browser yet),\n",
"// where there are multiple asynchronous steps and the Python side is going\n",
"// to poll for completion of each step.\n",
"// This uses a Promise to block the python side on completion of each step,\n",
"// then passes the result of the previous step as the input to the next step.\n",
"function _uploadFilesContinue(outputId) {\n",
" const outputElement = document.getElementById(outputId);\n",
" const steps = outputElement.steps;\n",
"\n",
" const next = steps.next(outputElement.lastPromiseValue);\n",
" return Promise.resolve(next.value.promise).then((value) => {\n",
" // Cache the last promise value to make it available to the next\n",
" // step of the generator.\n",
" outputElement.lastPromiseValue = value;\n",
" return next.value.response;\n",
" });\n",
"}\n",
"\n",
"/**\n",
" * Generator function which is called between each async step of the upload\n",
" * process.\n",
" * @param {string} inputId Element ID of the input file picker element.\n",
" * @param {string} outputId Element ID of the output display.\n",
" * @return {!Iterable<!Object>} Iterable of next steps.\n",
" */\n",
"function* uploadFilesStep(inputId, outputId) {\n",
" const inputElement = document.getElementById(inputId);\n",
" inputElement.disabled = false;\n",
"\n",
" const outputElement = document.getElementById(outputId);\n",
" outputElement.innerHTML = '';\n",
"\n",
" const pickedPromise = new Promise((resolve) => {\n",
" inputElement.addEventListener('change', (e) => {\n",
" resolve(e.target.files);\n",
" });\n",
" });\n",
"\n",
" const cancel = document.createElement('button');\n",
" inputElement.parentElement.appendChild(cancel);\n",
" cancel.textContent = 'Cancel upload';\n",
" const cancelPromise = new Promise((resolve) => {\n",
" cancel.onclick = () => {\n",
" resolve(null);\n",
" };\n",
" });\n",
"\n",
" // Wait for the user to pick the files.\n",
" const files = yield {\n",
" promise: Promise.race([pickedPromise, cancelPromise]),\n",
" response: {\n",
" action: 'starting',\n",
" }\n",
" };\n",
"\n",
" cancel.remove();\n",
"\n",
" // Disable the input element since further picks are not allowed.\n",
" inputElement.disabled = true;\n",
"\n",
" if (!files) {\n",
" return {\n",
" response: {\n",
" action: 'complete',\n",
" }\n",
" };\n",
" }\n",
"\n",
" for (const file of files) {\n",
" const li = document.createElement('li');\n",
" li.append(span(file.name, {fontWeight: 'bold'}));\n",
" li.append(span(\n",
" `(${file.type || 'n/a'}) - ${file.size} bytes, ` +\n",
" `last modified: ${\n",
" file.lastModifiedDate ? file.lastModifiedDate.toLocaleDateString() :\n",
" 'n/a'} - `));\n",
" const percent = span('0% done');\n",
" li.appendChild(percent);\n",
"\n",
" outputElement.appendChild(li);\n",
"\n",
" const fileDataPromise = new Promise((resolve) => {\n",
" const reader = new FileReader();\n",
" reader.onload = (e) => {\n",
" resolve(e.target.result);\n",
" };\n",
" reader.readAsArrayBuffer(file);\n",
" });\n",
" // Wait for the data to be ready.\n",
" let fileData = yield {\n",
" promise: fileDataPromise,\n",
" response: {\n",
" action: 'continue',\n",
" }\n",
" };\n",
"\n",
" // Use a chunked sending to avoid message size limits. See b/62115660.\n",
" let position = 0;\n",
" do {\n",
" const length = Math.min(fileData.byteLength - position, MAX_PAYLOAD_SIZE);\n",
" const chunk = new Uint8Array(fileData, position, length);\n",
" position += length;\n",
"\n",
" const base64 = btoa(String.fromCharCode.apply(null, chunk));\n",
" yield {\n",
" response: {\n",
" action: 'append',\n",
" file: file.name,\n",
" data: base64,\n",
" },\n",
" };\n",
"\n",
" let percentDone = fileData.byteLength === 0 ?\n",
" 100 :\n",
" Math.round((position / fileData.byteLength) * 100);\n",
" percent.textContent = `${percentDone}% done`;\n",
"\n",
" } while (position < fileData.byteLength);\n",
" }\n",
"\n",
" // All done.\n",
" yield {\n",
" response: {\n",
" action: 'complete',\n",
" }\n",
" };\n",
"}\n",
"\n",
"scope.google = scope.google || {};\n",
"scope.google.colab = scope.google.colab || {};\n",
"scope.google.colab._files = {\n",
" _uploadFiles,\n",
" _uploadFilesContinue,\n",
"};\n",
"})(self);\n",
"</script> "
]
},
"metadata": {}
},
{
"output_type": "stream",
"name": "stdout",
"text": [
"Saving league_tables.csv to league_tables.csv\n",
"User uploaded file \"league_tables.csv\" with length 35307 bytes\n"
]
}
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "df743865-c0b1-4108-b972-1714183751c8",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 206
},
"id": "df743865-c0b1-4108-b972-1714183751c8",
"outputId": "9eb5ba8d-7fbd-4176-b696-293d413a577f"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" Season_End_Year Team Rk MP W D L GF GA GD Pts \\\n",
"0 1993 Arsenal 10 42 15 11 16 40 38 2 56 \n",
"1 1993 Aston Villa 2 42 21 11 10 57 40 17 74 \n",
"2 1993 Blackburn 4 42 20 11 11 68 46 22 71 \n",
"3 1993 Chelsea 11 42 14 14 14 51 54 -3 56 \n",
"4 1993 Coventry City 15 42 13 13 16 52 57 -5 52 \n",
"\n",
" Notes \n",
"0 → European Cup Winners' Cup via cup win 2 \n",
"1 → UEFA Cup via league finish \n",
"2 NaN \n",
"3 NaN \n",
"4 NaN "
],
"text/html": [
"\n",
" <div id=\"df-75755398-5385-447b-955e-044c56f1a097\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Season_End_Year</th>\n",
" <th>Team</th>\n",
" <th>Rk</th>\n",
" <th>MP</th>\n",
" <th>W</th>\n",
" <th>D</th>\n",
" <th>L</th>\n",
" <th>GF</th>\n",
" <th>GA</th>\n",
" <th>GD</th>\n",
" <th>Pts</th>\n",
" <th>Notes</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1993</td>\n",
" <td>Arsenal</td>\n",
" <td>10</td>\n",
" <td>42</td>\n",
" <td>15</td>\n",
" <td>11</td>\n",
" <td>16</td>\n",
" <td>40</td>\n",
" <td>38</td>\n",
" <td>2</td>\n",
" <td>56</td>\n",
" <td>→ European Cup Winners' Cup via cup win 2</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>1993</td>\n",
" <td>Aston Villa</td>\n",
" <td>2</td>\n",
" <td>42</td>\n",
" <td>21</td>\n",
" <td>11</td>\n",
" <td>10</td>\n",
" <td>57</td>\n",
" <td>40</td>\n",
" <td>17</td>\n",
" <td>74</td>\n",
" <td>→ UEFA Cup via league finish</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>1993</td>\n",
" <td>Blackburn</td>\n",
" <td>4</td>\n",
" <td>42</td>\n",
" <td>20</td>\n",
" <td>11</td>\n",
" <td>11</td>\n",
" <td>68</td>\n",
" <td>46</td>\n",
" <td>22</td>\n",
" <td>71</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>1993</td>\n",
" <td>Chelsea</td>\n",
" <td>11</td>\n",
" <td>42</td>\n",
" <td>14</td>\n",
" <td>14</td>\n",
" <td>14</td>\n",
" <td>51</td>\n",
" <td>54</td>\n",
" <td>-3</td>\n",
" <td>56</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>1993</td>\n",
" <td>Coventry City</td>\n",
" <td>15</td>\n",
" <td>42</td>\n",
" <td>13</td>\n",
" <td>13</td>\n",
" <td>16</td>\n",
" <td>52</td>\n",
" <td>57</td>\n",
" <td>-5</td>\n",
" <td>52</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-75755398-5385-447b-955e-044c56f1a097')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-75755398-5385-447b-955e-044c56f1a097 button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-75755398-5385-447b-955e-044c56f1a097');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-838a516d-90e1-4aa9-af03-ffd0aaa86156\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-838a516d-90e1-4aa9-af03-ffd0aaa86156')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-838a516d-90e1-4aa9-af03-ffd0aaa86156 button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 17
}
],
"source": [
"df = pd.read_csv('league_tables.csv')\n",
"df.head()"
]
},
{
"cell_type": "markdown",
"id": "ac59b120-20d7-4865-94b0-0892b3ed1ddb",
"metadata": {
"id": "ac59b120-20d7-4865-94b0-0892b3ed1ddb"
},
"source": [
"**2.1 Preprocess the data to include stats only for Liverpool and Manchester Utd in df. [5 points]**\n",
"\n",
"Removing irrelevant rows and columns is usually a good practice for a data scientist."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "6776f2f0-c88f-42f7-ae96-edb3669b463d",
"metadata": {
"id": "6776f2f0-c88f-42f7-ae96-edb3669b463d"
},
"outputs": [],
"source": [
"df = df[df['Team'].isin(['Liverpool', 'Manchester Utd'])]"
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "a2ceebca-af90-42c1-ab67-268e0de572e9",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 206
},
"id": "a2ceebca-af90-42c1-ab67-268e0de572e9",
"outputId": "bf6faa88-83b5-47e5-e1d4-a8d6d21fdaca"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" Season_End_Year Team Rk MP W D L GF GA GD Pts \\\n",
"9 1993 Liverpool 6 42 16 11 15 62 55 7 59 \n",
"11 1993 Manchester Utd 1 42 24 12 6 67 31 36 84 \n",
"30 1994 Liverpool 8 42 17 9 16 59 55 4 60 \n",
"32 1994 Manchester Utd 1 42 27 11 4 80 38 42 92 \n",
"54 1995 Liverpool 4 42 21 11 10 65 37 28 74 \n",
"\n",
" Notes \n",
"9 NaN \n",
"11 → Champions League via league finish \n",
"30 NaN \n",
"32 → Champions League via league finish \n",
"54 → UEFA Cup via league finish "
],
"text/html": [
"\n",
" <div id=\"df-7fa65421-77fc-4bc8-8c1f-44219a4d8dc3\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Season_End_Year</th>\n",
" <th>Team</th>\n",
" <th>Rk</th>\n",
" <th>MP</th>\n",
" <th>W</th>\n",
" <th>D</th>\n",
" <th>L</th>\n",
" <th>GF</th>\n",
" <th>GA</th>\n",
" <th>GD</th>\n",
" <th>Pts</th>\n",
" <th>Notes</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>9</th>\n",
" <td>1993</td>\n",
" <td>Liverpool</td>\n",
" <td>6</td>\n",
" <td>42</td>\n",
" <td>16</td>\n",
" <td>11</td>\n",
" <td>15</td>\n",
" <td>62</td>\n",
" <td>55</td>\n",
" <td>7</td>\n",
" <td>59</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>11</th>\n",
" <td>1993</td>\n",
" <td>Manchester Utd</td>\n",
" <td>1</td>\n",
" <td>42</td>\n",
" <td>24</td>\n",
" <td>12</td>\n",
" <td>6</td>\n",
" <td>67</td>\n",
" <td>31</td>\n",
" <td>36</td>\n",
" <td>84</td>\n",
" <td>→ Champions League via league finish</td>\n",
" </tr>\n",
" <tr>\n",
" <th>30</th>\n",
" <td>1994</td>\n",
" <td>Liverpool</td>\n",
" <td>8</td>\n",
" <td>42</td>\n",
" <td>17</td>\n",
" <td>9</td>\n",
" <td>16</td>\n",
" <td>59</td>\n",
" <td>55</td>\n",
" <td>4</td>\n",
" <td>60</td>\n",
" <td>NaN</td>\n",
" </tr>\n",
" <tr>\n",
" <th>32</th>\n",
" <td>1994</td>\n",
" <td>Manchester Utd</td>\n",
" <td>1</td>\n",
" <td>42</td>\n",
" <td>27</td>\n",
" <td>11</td>\n",
" <td>4</td>\n",
" <td>80</td>\n",
" <td>38</td>\n",
" <td>42</td>\n",
" <td>92</td>\n",
" <td>→ Champions League via league finish</td>\n",
" </tr>\n",
" <tr>\n",
" <th>54</th>\n",
" <td>1995</td>\n",
" <td>Liverpool</td>\n",
" <td>4</td>\n",
" <td>42</td>\n",
" <td>21</td>\n",
" <td>11</td>\n",
" <td>10</td>\n",
" <td>65</td>\n",
" <td>37</td>\n",
" <td>28</td>\n",
" <td>74</td>\n",
" <td>→ UEFA Cup via league finish</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-7fa65421-77fc-4bc8-8c1f-44219a4d8dc3')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-7fa65421-77fc-4bc8-8c1f-44219a4d8dc3 button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-7fa65421-77fc-4bc8-8c1f-44219a4d8dc3');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-9c4789d5-c79a-409f-8493-df8a7905599e\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-9c4789d5-c79a-409f-8493-df8a7905599e')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-9c4789d5-c79a-409f-8493-df8a7905599e button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 19
}
],
"source": [
"df.head()"
]
},
{
"cell_type": "markdown",
"id": "2b7bdfcf-44b3-46b1-b40c-3a9f65870356",
"metadata": {
"id": "2b7bdfcf-44b3-46b1-b40c-3a9f65870356"
},
"source": [
"Here are two dataframes contain the values for Liverpool and Man Utd only for easier calculations."
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "12e0e4cd-0278-4a87-9514-fa7ae372aa2b",
"metadata": {
"id": "12e0e4cd-0278-4a87-9514-fa7ae372aa2b"
},
"outputs": [],
"source": [
"liverpool = df[df['Team'].isin(['Liverpool'])]\n",
"man_utd = df[df['Team'].isin(['Manchester Utd'])]"
]
},
{
"cell_type": "markdown",
"id": "1e107bda-02ac-47b5-bb97-d2b1ccdd9abb",
"metadata": {
"id": "1e107bda-02ac-47b5-bb97-d2b1ccdd9abb"
},
"source": [
"**2.2 Calculate the average goal-scoring rate for Liverpool and Manchester United. [5 points]**"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "c4898d75-59db-437f-ac2c-901b68028ab4",
"metadata": {
"id": "c4898d75-59db-437f-ac2c-901b68028ab4"
},
"outputs": [],
"source": [
"# Average goal-scoring rate for Liverpool\n",
"liv_avg = liverpool[\"GF\"].sum() / liverpool[\"MP\"].sum()\n",
"\n",
"# Average goal-scoring rate for Manchester United\n",
"man_avg = man_utd[\"GF\"].sum() / man_utd[\"MP\"].sum()"
]
},
{
"cell_type": "markdown",
"id": "2bf49280-ac5f-451c-b6eb-276add2142d6",
"metadata": {
"id": "2bf49280-ac5f-451c-b6eb-276add2142d6"
},
"source": [
"**2.3 Fitting gamma distribution for Liverpool [7 points]**"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "73acdbe0-5cf5-44df-a384-0e5152f9946c",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 459
},
"id": "73acdbe0-5cf5-44df-a384-0e5152f9946c",
"outputId": "22e721b0-4d16-4714-ac35-20ca3209180a"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {}
}
],
"source": [
"from scipy.stats import gamma\n",
"\n",
"# Calculate the gamma distribution values for Liverpool\n",
"liv_gamma = [gamma.pdf(lam, liv_avg) for lam in np.arange(0, 10, .1)]\n",
"\n",
"# Plot the gamma distribution values for Liverpool\n",
"plt.plot(np.arange(0, 10, .1), liv_gamma/sum(liv_gamma), color=\"red\")\n",
"plt.xlabel('Goal Scoring Rate $\\lambda$', size = 16)\n",
"plt.ylabel('Probability', size = 16)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "d8e67d44-139c-424e-b577-5383536e0ce8",
"metadata": {
"id": "d8e67d44-139c-424e-b577-5383536e0ce8"
},
"source": [
"**2.4 Fitting the gamma distribution for Manchester United [7 points]**"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "8b287395-fd12-40dc-aecf-2cb1d5c8d4c9",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 460
},
"id": "8b287395-fd12-40dc-aecf-2cb1d5c8d4c9",
"outputId": "81224d97-5cc7-408a-85ab-67c266dc5ecf"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {}
}
],
"source": [
"# Calculate the gamma distribution values for Manchester Utd\n",
"man_gamma = [gamma.pdf(lam, man_avg) for lam in np.arange(0, 10, .1)]\n",
"\n",
"# Plot the gamma distribution values for Manchester Utd\n",
"plt.plot(np.arange(0, 10, .1), man_gamma/sum(man_gamma), color=\"blue\")\n",
"plt.xlabel('Goal Scoring Rate $\\lambda$', size = 16)\n",
"plt.ylabel('Probability', size = 16)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "bb0d52d6-6404-42bc-88fa-55994eb17b87",
"metadata": {
"id": "bb0d52d6-6404-42bc-88fa-55994eb17b87"
},
"source": [
"**2.5 Defining likelihood and update [8 points]**"
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "b9977e53-47f9-439c-81f5-b34902252aab",
"metadata": {
"id": "b9977e53-47f9-439c-81f5-b34902252aab"
},
"outputs": [],
"source": [
"# Function for poisson likelihood\n",
"def likelihood_poisson(lam, data):\n",
" '''Returns the likelihood of seeing k goals for goal scoring rate lambda'''\n",
" return [poisson.pmf(data, l) for l in lam]\n",
"\n",
"# Bayesian update function\n",
"def update(distribution, likelihood):\n",
" '''our standard Bayesian update function'''\n",
" distribution *= likelihood # Multiply the prior with the likelihood\n",
" prob_data = distribution.sum() # Normalizing constant\n",
" distribution /= prob_data # Normalize the distribution to get the posterior\n",
" return distribution"
]
},
{
"cell_type": "markdown",
"id": "977a695f-5807-4fe4-b3aa-d4f60d696c37",
"metadata": {
"id": "977a695f-5807-4fe4-b3aa-d4f60d696c37"
},
"source": [
"**2.6 Updating for Liverpool [5 points]**"
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "edb98a14-3866-45eb-bdcd-9d2af198ff7e",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 459
},
"id": "edb98a14-3866-45eb-bdcd-9d2af198ff7e",
"outputId": "a9d9738b-4cb1-446f-c2ee-88b3c195feaf"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {}
}
],
"source": [
"# Creating the prior for Liverpool based on gamma distribution\n",
"prior = pd.DataFrame({'lams':np.arange(0, 10, .1),'probs':liv_gamma/sum(liv_gamma)})\n",
"liv = prior.copy()\n",
"\n",
"# Update the prior based on new data for Liverpool\n",
"update(liv['probs'], likelihood_poisson(liv['lams'], 7))\n",
"\n",
"# Plot the updated distribution for Liverpool\n",
"plt.plot(prior['lams'], prior['probs'], color=\"gray\")\n",
"plt.plot(liv['lams'], liv['probs'], color=\"red\")\n",
"plt.legend(['Prior', 'Liverpool Posterior'], fontsize = 14, loc = 'best')\n",
"plt.xlabel('Goal Scoring Rate $\\lambda$', size = 16)\n",
"plt.ylabel('Probability', size = 16)\n",
"plt.show()"
]
},
{
"cell_type": "markdown",
"id": "c0878a0e-70f6-4972-b840-08687f3a7782",
"metadata": {
"id": "c0878a0e-70f6-4972-b840-08687f3a7782"
},
"source": [
"**2.7 Updating for Manchester United [5 points]**"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "410095f1-e370-498f-87b2-e147ac1a6d9d",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "410095f1-e370-498f-87b2-e147ac1a6d9d",
"outputId": "9557d740-ac8a-4411-b8d6-f4c8f69c7baf"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"0 0.000000e+00\n",
"1 4.045798e-02\n",
"2 6.167076e-02\n",
"3 7.263094e-02\n",
"4 7.696540e-02\n",
" ... \n",
"95 1.643219e-08\n",
"96 1.358046e-08\n",
"97 1.122254e-08\n",
"98 9.273132e-09\n",
"99 7.661630e-09\n",
"Name: probs, Length: 100, dtype: float64"
]
},
"metadata": {},
"execution_count": 26
}
],
"source": [
"prior = pd.DataFrame({'lams':np.arange(0, 10, .1),'probs':man_gamma/sum(man_gamma)})\n",
"man = prior.copy()\n",
"\n",
"# Update the prior based on new data for Manchester Utd (0 goals)\n",
"update(man['probs'], likelihood_poisson(man['lams'], 0))"
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "4aa53b85-b600-4bf3-8e04-4e8788f24501",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 461
},
"id": "4aa53b85-b600-4bf3-8e04-4e8788f24501",
"outputId": "c6fc0bc5-fef4-4509-bb25-83b522469633"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {}
}
],
"source": [
"# Plot the updated distribution for Manchester Utd\n",
"plt.plot(prior['lams'], prior['probs'], color=\"gray\")\n",
"plt.plot(man['lams'], man['probs'], color=\"blue\")\n",
"plt.legend(['Prior', 'Manchester Utd Posterior'], fontsize = 14, loc = 'best')\n",
"plt.xlabel('Goal Scoring Rate $\\lambda$', size = 16)\n",
"plt.ylabel('Probability', size = 16)\n",
"plt.show()"
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "e613b203-5cd8-486a-abe7-4255544e7c9c",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 461
},
"id": "e613b203-5cd8-486a-abe7-4255544e7c9c",
"outputId": "a9ed42a2-5348-4c32-9fb5-33028361768b"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "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\n"
},
"metadata": {}
}
],
"source": [
"# Plotting Liverpool and Manchester Utd together\n",
"plt.plot(liv['lams'], liv['probs'], color=\"red\")\n",
"plt.plot(man['lams'], man['probs'], color=\"blue\")\n",
"plt.legend(['Liverpool', 'Manchester Utd'], fontsize = 14, loc = 'best')\n",
"plt.xlabel('Goal Scoring Rate $\\lambda$', size = 16)\n",
"plt.ylabel('Probability', size = 16);"
]
},
{
"cell_type": "markdown",
"id": "6c152837-88f6-4e70-9c99-ba660bef59de",
"metadata": {
"id": "6c152837-88f6-4e70-9c99-ba660bef59de"
},
"source": [
"**2.8 What is the probability that a random value drawn from Liverpool’s distribution exceeds a value drawn from Man Utd’s distribution? [10\n",
"points] - BONUS**"
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "c018dfd0-e8eb-42a2-8883-70e585a18ca6",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/"
},
"id": "c018dfd0-e8eb-42a2-8883-70e585a18ca6",
"outputId": "82f33bbf-46d9-4db6-9509-be105a4433b8"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
"0.9881552082826743"
]
},
"metadata": {},
"execution_count": 29
}
],
"source": [
"# Function to compute the probability of superiority\n",
"def prob_of_s(dist1, dist2):\n",
" total = 0\n",
" # Iterate over each row in the first distribution 'dist1'\n",
" for index1, row1 in dist1.iterrows():\n",
" # Iterate over each row in the second distribution 'dist2'\n",
" for index2, row2 in dist2.iterrows():\n",
" # Check if the lambda value of the first row is greater than that of the second row\n",
" if row1['lams'] > row2['lams']:\n",
" # Update the 'total' variable by adding the product of probabilities of both rows\n",
" total += row1['probs'] * row2['probs']\n",
" return total\n",
"\n",
"# Calculate and print the probability of superiority of the 'liv' over the 'man' distributions\n",
"prob_of_s(liv, man)"
]
},
{
"cell_type": "markdown",
"id": "50136534-381c-49cb-9919-ded283b5874a",
"metadata": {
"id": "50136534-381c-49cb-9919-ded283b5874a"
},
"source": [
"**2.9 If the same teams played again, what is the chance Liverpool would win again? [8 points] - BONUS**"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "ddc490fb-13a3-47c8-a144-e035c5581168",
"metadata": {
"id": "ddc490fb-13a3-47c8-a144-e035c5581168"
},
"outputs": [],
"source": [
"def make_mixture(pmf_table, probs):\n",
" \"\"\"Make a mixture of distributions.\"\"\"\n",
" # Multiply the 'pmf_table' by 'probs', transpose the result, and then sum along the specified axis\n",
" # mix = ...\n",
" mix = (pmf_table.transpose().multiply(probs)).sum(axis=1)\n",
" return mix"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "420aa58c-5901-45d4-badb-fc082beab026",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 424
},
"id": "420aa58c-5901-45d4-badb-fc082beab026",
"outputId": "e7a12e52-5472-4e1a-b3c8-b8d8e4608ba5"
},
"outputs": [
{
"output_type": "execute_result",
"data": {
"text/plain": [
" 0 1 2 3 4 5 \\\n",
"0 1.000000 0.000000 0.000000 0.000000 0.000000 0.000000e+00 \n",
"1 0.904837 0.090484 0.004524 0.000151 0.000004 7.540312e-08 \n",
"2 0.818731 0.163746 0.016375 0.001092 0.000055 2.183282e-06 \n",
"3 0.740818 0.222245 0.033337 0.003334 0.000250 1.500157e-05 \n",
"4 0.670320 0.268128 0.053626 0.007150 0.000715 5.720064e-05 \n",
".. ... ... ... ... ... ... \n",
"95 0.000143 0.001363 0.006473 0.020497 0.048681 9.249398e-02 \n",
"96 0.000133 0.001278 0.006133 0.019626 0.047103 9.043735e-02 \n",
"97 0.000124 0.001199 0.005813 0.018795 0.045578 8.842148e-02 \n",
"98 0.000115 0.001125 0.005511 0.018002 0.044105 8.644639e-02 \n",
"99 0.000107 0.001056 0.005226 0.017246 0.042683 8.451198e-02 \n",
"\n",
" 6 7 8 9 \n",
"0 0.000000e+00 0.000000e+00 0.000000e+00 0.000000e+00 \n",
"1 1.256719e-09 1.795312e-11 2.244140e-13 2.493489e-15 \n",
"2 7.277607e-08 2.079316e-09 5.198290e-11 1.155176e-12 \n",
"3 7.500784e-07 3.214622e-08 1.205483e-09 4.018277e-11 \n",
"4 3.813376e-06 2.179072e-07 1.089536e-08 4.842383e-10 \n",
".. ... ... ... ... \n",
"95 1.464488e-01 1.987519e-01 2.360179e-01 2.491300e-01 \n",
"96 1.446998e-01 1.984454e-01 2.381345e-01 2.540101e-01 \n",
"97 1.429481e-01 1.980852e-01 2.401783e-01 2.588588e-01 \n",
"98 1.411958e-01 1.976741e-01 2.421507e-01 2.636753e-01 \n",
"99 1.394448e-01 1.972147e-01 2.440532e-01 2.684586e-01 \n",
"\n",
"[100 rows x 10 columns]"
],
"text/html": [
"\n",
" <div id=\"df-1bbc7aff-e93b-4f7f-b140-62c9dd626183\" class=\"colab-df-container\">\n",
" <div>\n",
"<style scoped>\n",
" .dataframe tbody tr th:only-of-type {\n",
" vertical-align: middle;\n",
" }\n",
"\n",
" .dataframe tbody tr th {\n",
" vertical-align: top;\n",
" }\n",
"\n",
" .dataframe thead th {\n",
" text-align: right;\n",
" }\n",
"</style>\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>0</th>\n",
" <th>1</th>\n",
" <th>2</th>\n",
" <th>3</th>\n",
" <th>4</th>\n",
" <th>5</th>\n",
" <th>6</th>\n",
" <th>7</th>\n",
" <th>8</th>\n",
" <th>9</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td>1.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000</td>\n",
" <td>0.000000e+00</td>\n",
" <td>0.000000e+00</td>\n",
" <td>0.000000e+00</td>\n",
" <td>0.000000e+00</td>\n",
" <td>0.000000e+00</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td>0.904837</td>\n",
" <td>0.090484</td>\n",
" <td>0.004524</td>\n",
" <td>0.000151</td>\n",
" <td>0.000004</td>\n",
" <td>7.540312e-08</td>\n",
" <td>1.256719e-09</td>\n",
" <td>1.795312e-11</td>\n",
" <td>2.244140e-13</td>\n",
" <td>2.493489e-15</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td>0.818731</td>\n",
" <td>0.163746</td>\n",
" <td>0.016375</td>\n",
" <td>0.001092</td>\n",
" <td>0.000055</td>\n",
" <td>2.183282e-06</td>\n",
" <td>7.277607e-08</td>\n",
" <td>2.079316e-09</td>\n",
" <td>5.198290e-11</td>\n",
" <td>1.155176e-12</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td>0.740818</td>\n",
" <td>0.222245</td>\n",
" <td>0.033337</td>\n",
" <td>0.003334</td>\n",
" <td>0.000250</td>\n",
" <td>1.500157e-05</td>\n",
" <td>7.500784e-07</td>\n",
" <td>3.214622e-08</td>\n",
" <td>1.205483e-09</td>\n",
" <td>4.018277e-11</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td>0.670320</td>\n",
" <td>0.268128</td>\n",
" <td>0.053626</td>\n",
" <td>0.007150</td>\n",
" <td>0.000715</td>\n",
" <td>5.720064e-05</td>\n",
" <td>3.813376e-06</td>\n",
" <td>2.179072e-07</td>\n",
" <td>1.089536e-08</td>\n",
" <td>4.842383e-10</td>\n",
" </tr>\n",
" <tr>\n",
" <th>...</th>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" <td>...</td>\n",
" </tr>\n",
" <tr>\n",
" <th>95</th>\n",
" <td>0.000143</td>\n",
" <td>0.001363</td>\n",
" <td>0.006473</td>\n",
" <td>0.020497</td>\n",
" <td>0.048681</td>\n",
" <td>9.249398e-02</td>\n",
" <td>1.464488e-01</td>\n",
" <td>1.987519e-01</td>\n",
" <td>2.360179e-01</td>\n",
" <td>2.491300e-01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>96</th>\n",
" <td>0.000133</td>\n",
" <td>0.001278</td>\n",
" <td>0.006133</td>\n",
" <td>0.019626</td>\n",
" <td>0.047103</td>\n",
" <td>9.043735e-02</td>\n",
" <td>1.446998e-01</td>\n",
" <td>1.984454e-01</td>\n",
" <td>2.381345e-01</td>\n",
" <td>2.540101e-01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>97</th>\n",
" <td>0.000124</td>\n",
" <td>0.001199</td>\n",
" <td>0.005813</td>\n",
" <td>0.018795</td>\n",
" <td>0.045578</td>\n",
" <td>8.842148e-02</td>\n",
" <td>1.429481e-01</td>\n",
" <td>1.980852e-01</td>\n",
" <td>2.401783e-01</td>\n",
" <td>2.588588e-01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>98</th>\n",
" <td>0.000115</td>\n",
" <td>0.001125</td>\n",
" <td>0.005511</td>\n",
" <td>0.018002</td>\n",
" <td>0.044105</td>\n",
" <td>8.644639e-02</td>\n",
" <td>1.411958e-01</td>\n",
" <td>1.976741e-01</td>\n",
" <td>2.421507e-01</td>\n",
" <td>2.636753e-01</td>\n",
" </tr>\n",
" <tr>\n",
" <th>99</th>\n",
" <td>0.000107</td>\n",
" <td>0.001056</td>\n",
" <td>0.005226</td>\n",
" <td>0.017246</td>\n",
" <td>0.042683</td>\n",
" <td>8.451198e-02</td>\n",
" <td>1.394448e-01</td>\n",
" <td>1.972147e-01</td>\n",
" <td>2.440532e-01</td>\n",
" <td>2.684586e-01</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"<p>100 rows × 10 columns</p>\n",
"</div>\n",
" <div class=\"colab-df-buttons\">\n",
"\n",
" <div class=\"colab-df-container\">\n",
" <button class=\"colab-df-convert\" onclick=\"convertToInteractive('df-1bbc7aff-e93b-4f7f-b140-62c9dd626183')\"\n",
" title=\"Convert this dataframe to an interactive table.\"\n",
" style=\"display:none;\">\n",
"\n",
" <svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\" viewBox=\"0 -960 960 960\">\n",
" <path d=\"M120-120v-720h720v720H120Zm60-500h600v-160H180v160Zm220 220h160v-160H400v160Zm0 220h160v-160H400v160ZM180-400h160v-160H180v160Zm440 0h160v-160H620v160ZM180-180h160v-160H180v160Zm440 0h160v-160H620v160Z\"/>\n",
" </svg>\n",
" </button>\n",
"\n",
" <style>\n",
" .colab-df-container {\n",
" display:flex;\n",
" gap: 12px;\n",
" }\n",
"\n",
" .colab-df-convert {\n",
" background-color: #E8F0FE;\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: #1967D2;\n",
" height: 32px;\n",
" padding: 0 0 0 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-convert:hover {\n",
" background-color: #E2EBFA;\n",
" box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: #174EA6;\n",
" }\n",
"\n",
" .colab-df-buttons div {\n",
" margin-bottom: 4px;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert {\n",
" background-color: #3B4455;\n",
" fill: #D2E3FC;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-convert:hover {\n",
" background-color: #434B5C;\n",
" box-shadow: 0px 1px 3px 1px rgba(0, 0, 0, 0.15);\n",
" filter: drop-shadow(0px 1px 2px rgba(0, 0, 0, 0.3));\n",
" fill: #FFFFFF;\n",
" }\n",
" </style>\n",
"\n",
" <script>\n",
" const buttonEl =\n",
" document.querySelector('#df-1bbc7aff-e93b-4f7f-b140-62c9dd626183 button.colab-df-convert');\n",
" buttonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
"\n",
" async function convertToInteractive(key) {\n",
" const element = document.querySelector('#df-1bbc7aff-e93b-4f7f-b140-62c9dd626183');\n",
" const dataTable =\n",
" await google.colab.kernel.invokeFunction('convertToInteractive',\n",
" [key], {});\n",
" if (!dataTable) return;\n",
"\n",
" const docLinkHtml = 'Like what you see? Visit the ' +\n",
" '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
" + ' to learn more about interactive tables.';\n",
" element.innerHTML = '';\n",
" dataTable['output_type'] = 'display_data';\n",
" await google.colab.output.renderOutput(dataTable, element);\n",
" const docLink = document.createElement('div');\n",
" docLink.innerHTML = docLinkHtml;\n",
" element.appendChild(docLink);\n",
" }\n",
" </script>\n",
" </div>\n",
"\n",
"\n",
"<div id=\"df-bceafe9f-91f5-4aa1-ad84-cf6d9eb89e1b\">\n",
" <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-bceafe9f-91f5-4aa1-ad84-cf6d9eb89e1b')\"\n",
" title=\"Suggest charts.\"\n",
" style=\"display:none;\">\n",
"\n",
"<svg xmlns=\"http://www.w3.org/2000/svg\" height=\"24px\"viewBox=\"0 0 24 24\"\n",
" width=\"24px\">\n",
" <g>\n",
" <path d=\"M19 3H5c-1.1 0-2 .9-2 2v14c0 1.1.9 2 2 2h14c1.1 0 2-.9 2-2V5c0-1.1-.9-2-2-2zM9 17H7v-7h2v7zm4 0h-2V7h2v10zm4 0h-2v-4h2v4z\"/>\n",
" </g>\n",
"</svg>\n",
" </button>\n",
"\n",
"<style>\n",
" .colab-df-quickchart {\n",
" --bg-color: #E8F0FE;\n",
" --fill-color: #1967D2;\n",
" --hover-bg-color: #E2EBFA;\n",
" --hover-fill-color: #174EA6;\n",
" --disabled-fill-color: #AAA;\n",
" --disabled-bg-color: #DDD;\n",
" }\n",
"\n",
" [theme=dark] .colab-df-quickchart {\n",
" --bg-color: #3B4455;\n",
" --fill-color: #D2E3FC;\n",
" --hover-bg-color: #434B5C;\n",
" --hover-fill-color: #FFFFFF;\n",
" --disabled-bg-color: #3B4455;\n",
" --disabled-fill-color: #666;\n",
" }\n",
"\n",
" .colab-df-quickchart {\n",
" background-color: var(--bg-color);\n",
" border: none;\n",
" border-radius: 50%;\n",
" cursor: pointer;\n",
" display: none;\n",
" fill: var(--fill-color);\n",
" height: 32px;\n",
" padding: 0;\n",
" width: 32px;\n",
" }\n",
"\n",
" .colab-df-quickchart:hover {\n",
" background-color: var(--hover-bg-color);\n",
" box-shadow: 0 1px 2px rgba(60, 64, 67, 0.3), 0 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
" fill: var(--button-hover-fill-color);\n",
" }\n",
"\n",
" .colab-df-quickchart-complete:disabled,\n",
" .colab-df-quickchart-complete:disabled:hover {\n",
" background-color: var(--disabled-bg-color);\n",
" fill: var(--disabled-fill-color);\n",
" box-shadow: none;\n",
" }\n",
"\n",
" .colab-df-spinner {\n",
" border: 2px solid var(--fill-color);\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" animation:\n",
" spin 1s steps(1) infinite;\n",
" }\n",
"\n",
" @keyframes spin {\n",
" 0% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" border-left-color: var(--fill-color);\n",
" }\n",
" 20% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 30% {\n",
" border-color: transparent;\n",
" border-left-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 40% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-top-color: var(--fill-color);\n",
" }\n",
" 60% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" }\n",
" 80% {\n",
" border-color: transparent;\n",
" border-right-color: var(--fill-color);\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" 90% {\n",
" border-color: transparent;\n",
" border-bottom-color: var(--fill-color);\n",
" }\n",
" }\n",
"</style>\n",
"\n",
" <script>\n",
" async function quickchart(key) {\n",
" const quickchartButtonEl =\n",
" document.querySelector('#' + key + ' button');\n",
" quickchartButtonEl.disabled = true; // To prevent multiple clicks.\n",
" quickchartButtonEl.classList.add('colab-df-spinner');\n",
" try {\n",
" const charts = await google.colab.kernel.invokeFunction(\n",
" 'suggestCharts', [key], {});\n",
" } catch (error) {\n",
" console.error('Error during call to suggestCharts:', error);\n",
" }\n",
" quickchartButtonEl.classList.remove('colab-df-spinner');\n",
" quickchartButtonEl.classList.add('colab-df-quickchart-complete');\n",
" }\n",
" (() => {\n",
" let quickchartButtonEl =\n",
" document.querySelector('#df-bceafe9f-91f5-4aa1-ad84-cf6d9eb89e1b button');\n",
" quickchartButtonEl.style.display =\n",
" google.colab.kernel.accessAllowed ? 'block' : 'none';\n",
" })();\n",
" </script>\n",
"</div>\n",
" </div>\n",
" </div>\n"
]
},
"metadata": {},
"execution_count": 31
}
],
"source": [
"pmf_table = pd.DataFrame([[poisson.pmf(goals,lam) for goals in range(10)] for lam in prior['lams']])\n",
"pmf_table = (pmf_table.T / pmf_table.T.sum()).T\n",
"pmf_table"
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "695841ee-4567-4f5d-9c93-b39ec0c0c054",
"metadata": {
"colab": {
"base_uri": "https://localhost:8080/",
"height": 455
},
"id": "695841ee-4567-4f5d-9c93-b39ec0c0c054",
"outputId": "4cd45adf-5fd2-4dda-9be3-79f73e356b7a"
},
"outputs": [
{
"output_type": "display_data",
"data": {
"text/plain": [
"<Figure size 640x480 with 1 Axes>"
],
"image/png": "iVBORw0KGgoAAAANSUhEUgAAAj0AAAG2CAYAAACUDjeHAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjcuMSwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy/bCgiHAAAACXBIWXMAAA9hAAAPYQGoP6dpAABuMElEQVR4nO3dd1gUVxcG8HeXjhQLgo1mib2j2NFoxNh7LFEsMbEX1ESTWKOxRI3GXrFHo59dQ1QitmBF7F0Ug4IdpEjb+f642UWkSFmYZff9Pc8+7M7OzhzqHu6ce65CkiQJRERERHpOKXcARERERHmBSQ8REREZBCY9REREZBCY9BAREZFBYNJDREREBoFJDxERERkEJj1ERERkEIzlDkBXqFQqPHnyBNbW1lAoFHKHQ0RERJkgSRLevn2LEiVKQKnMeCyHSc9/njx5AkdHR7nDICIiomx4/PgxSpUqleE+THr+Y21tDUB80WxsbGSOhoiIiDIjMjISjo6OmvfxjDDp+Y/6kpaNjQ2THiIionwmM6UpLGQmIiIig8Ckh4iIiAwCkx4iIiIyCEx6iIiIyCAw6SEiIiKDwKSHiIiIDAKnrBNRvpOQkICkpCS5wyCiXGJkZAQTExOtH5dJDxHlG5GRkXjx4gXi4uLkDoWIcpmZmRns7Oy02juPSQ8R5QuRkZEIDQ2FlZUV7OzsYGJiwnXyiPSQJElISEhAREQEQkNDAUBriQ+THiLKF168eAErKyuUKlWKyQ6RnrOwsIC1tTX+/fdfvHjxQmtJDwuZiUjnJSQkIC4uDra2tkx4iAyEQqGAra0t4uLikJCQoJVjMukhIp2nLlrOjcJGItJd6t95bU1cYNKTF54+Ba5ckTsKonyPozxEhkXbv/NMenLb//4HODkBgwfLHQkREZFBY9KT2xo2FB8DAoCgIFlDISIiMmRMenJbsWJAly7i/vLl8sZCRAbB398fCoUCU6dOlTsUnda0aVNeMjUwTHrywtCh4uPmzUBEhLyxEFG+9fDhQygUCrRq1UruUIjyJSY9eaFxY6ByZSAmBti4Ue5oiEjP1a1bFzdv3sTw4cPlDoVIpzDpyQsKBTBkiLi/fDkgSfLGQ0R6zdLSEhUqVICdnZ3coRDpFCY9eaVPH6BAAeDmTeD4cbmjISI9llZNT9myZWFtbY2YmJg0X9O+fXsoFArcuXMnxfa9e/eiefPmKFSoEMzNzVGlShXMmzcvVd+U9evXQ6FQYP369di/fz8aNmwIa2truLi4pIrp1KlTaNq0KaytrVGwYEF06dIF9+7dSzOua9euoXv37rC3t4eZmRlcXV0xevRovHz5Uiv7k2Fh0pNXbGyAL78U95ctkzcWIjI4X375JaKiorBnz55Uz7148QK+vr5wd3fHJ598otk+ceJEdOzYEbdv30bnzp0xdOhQWFhYYPz48ejRo0ea59mxYwc6d+4Me3t7DB06FJ9//nmK58+cOYPmzZvD1tYWI0aMgIeHB3bv3o0GDRrgwYMHKfY9deoU3N3dsXv3bjRv3hze3t5wdnbGokWL4O7ujhcvXuRofzJAEkmSJEkRERESACkiIiL3ThIUJEmAJBkbS9KTJ7l3HiI9ExsbK924cUOKjY1N9ZxKJUlRUbp/U6ly/nUIDg6WAEienp4Z7nfs2DEJgDRlyhTNtrt370oApM8//zzV/osXL5YASEuWLNFsO3z4sOZcUVFR7329VdLgwYMlANLOnTs12318fCQAklKplI4cOZJuTACkFStWpHhuxYoVEgCpbdu2mm1JSUlSmTJlJACSr69viv3Hjx8vAZAGDBiQ7f0lSZI8PDwkvg3qtox+99Wy8v7N7/Z/8iTpkSRJathQJD7Tp+fueYj0SEZ/+KKixK+Urt/eyxuyLSdJjyRJUv369SVjY2MpPDw8xfa6detKJiYm0vPnzzXb2rdvLwGQHj16lOr4b968kRQKhdSlSxfNNnXS06lTpwxj+uSTT6SkpKQUzyUlJUnlypWTFAqF9OzZM0mSJOnEiRPpJmlv376VChcuLJmbm0txcXHZ2l+SmPTkB9pOerjKel4bOhQ4fRpYuRKYOBEw5reAiPJGnz59EBAQgN9//x2jRo0CANy9exfnzp1Du3btUhQ+nzlzBgUKFMC6devSPJaFhQVu3bqVanvdunUzjKFhw4ZQKlNWViiVSjRs2BB3797F5cuX0aJFC1y6dAmA6KXzISsrK7i5ueHw4cO4ffs2qlatmuX9yTDxHTevdekCjB4NhIYCBw4AHTvKHRFRvmZpCURFyR3Fx1layh0B8MUXX2D06NHYvHmzJunZtGkTAJEQve/Vq1dITEzEtGnT0j1edHR0qm0ODg4ZxpDe8+rtEf/1MouMjMxw/+LFi6fYL6v7k2Fi0pPXzMyAgQOB2bNFQTOTHqIcUSjExEj6uMKFC6N169bYs2cPbt++jfLly2Pz5s2wtbVFu3btUuxrY2MDhUKR5eLfj3U4Dg8Pz3C7ra2t5vwZ7R8WFpZiv6zuT4aJs7fk8M034i/1kSPA3btyR0NEBkQ9orN582acPn0awcHB6Nq1K8zNzVPs5+7ujpcvX+Kulv9GnT59GiqVKsU2lUqFf/75BwqFAtWrVwcA1KxZE4CY6v6h6OhoXLhwARYWFihfvny29ifDxKRHDi4uQOvW4v6KFbKGQkSGpU2bNihUqBC2bNmCjf91iP/w0hYAjBw5EgAwYMCANHvchIWF4ebNm1k+/507d7B69eoU21avXo07d+6gTZs2KFq0KABR+1OmTBn8+eefOHr0aIr9Z8yYgZcvX6Jnz54wNTXN1v5kmHh5Sy5DhwIHDwI+PsBPP+nGBX8iyheuXr2Kfv36pflchQoVUK9evXRfa2Zmhu7du2PlypXw8fGBs7MzmjRpkmq/Vq1aYdKkSfjpp59QtmxZtGrVCs7Oznj58iXu3buHkydPYsaMGahYsWKWYvf09MTIkSNx6NAhVK5cGdevX8f+/fthZ2eHRYsWafZTKpVYv349PD090bp1a3Tr1g3Ozs4ICAiAv78/ypQpg9mzZ2d7fzJQ2pxalp/l2ZR1tcRESXJ1FXNZ163Lm3MS5VOZmbZqCNRT1jO6eXh4pDtlXe3UqVOa/SdOnJjhOY8cOSK1a9dOKlq0qGRiYiIVK1ZMql+/vvTTTz9JISEhmv3UU9Z9fHzSPM77MZ08eVLy8PCQChQoINnY2EidOnWS7t69m+brrly5InXt2lWys7OTTExMJGdnZ2nUqFEpptdnd39OWdd92p6yrpAkLgQFiIp+W1tbRERE5F2h25w5wIQJgJsbcP583pyTKB969+4dgoOD4erqmqr2hPIHf39/NGvWDFOmTEmxPAZRRjLzu5+V92/W9MhpwADA1BS4cIFJDxERUS5j0iOnokWB7t3F/eXL5Y2FiIhIzzHpkdvQoeLj778Dr17JGwsREZEe4+wtudWrB1SvDly+DGzYAIwZI3dERERa17RpU7CElOTGkR65KRTJoz3LlwMfNO0iIiIi7WDSowt69QJsbER3Zj8/uaMhIiLSS0x6dIGVFdC3r7jPgmYiIqJcwaRHVwwZIj7u3Qv8+6+8sRAREekhJj26olIloGlTUdOzapXc0RAREekdJj26RD3as3o1kJAgbyxERER6hkmPLunYEShWDAgLA/bskTsaIiIivcKkR5eYmgKDBon7y5bJGwsREZGeYdKja77+GjAyAvz9gRs35I6GiIhIbzDp0TWlSgHt2on7K1bIGwsRUS7p168fFAoFHj58KHcoBmfq1KlQKBTw9/eX5fzr16+HQqHA+vXr8/zcTHp0kbpD84YNQFSUvLEQkU54+PAhFAoFFAoFihUrhsTExDT3u3nzpmY/FxeXvA0yH/L394dCocDUqVN1Io5+/frlaJ/sUv985caxdQmTHl3UvDlQrhwQGQls3Sp3NESkQ4yNjREeHo5Dhw6l+fzatWuhVCqhVPLPO6Vt+PDhuHnzJurWrSt3KHmOvxW6SKkEBg8W95cvB7hIHxH9p0GDBrC1tcW6detSPZeYmIjNmzejRYsWMDExkSE6yg/s7OxQoUIFWFpayh1KnmPSo6v69QPMzYGgIODMGbmjISIdYWFhgR49euDgwYN49uxZiucOHDiA8PBwDBgwIM3XPnnyBFOmTEG9evVgb28PMzMzuLi4YOjQoamOBSTX3QQHB+O3335DhQoVYGZmBmdnZ0ybNg2qdBZI3rt3L1q2bIkiRYrA3NwcLi4u6NOnD65du5ZqX0mSsnzs5s2bo1ChQjA3N0eVKlUwb948JCUlpdhPpVJhzZo1qFu3LgoXLgwLCwuUKlUK7dq109SyTJ06Fc2aNQMATJs2TXNZ8MNao/j4eCxYsAC1atVCgQIFYG1tjcaNG2Pfvn3pfs0ePHiA+fPno1KlSjAzM8vVy0YuLi5wcXFBVFQURo0ahRIlSsDMzAzVqlXDzp07U+3/YU3P+vXr4erqCgDYsGFDiq/D+3U/kiRh3bp1aNiwIWxsbGBpaQk3N7c0E3AAePXqFQYPHgwHBwdYWlqiTp062L17t9Y//6wwlvXslL7ChYGePQEfHzF9vX59uSMiIh0xYMAArFy5Eps2bcLYsWM129etW4fChQujY8eOab7uxIkTmD9/Ppo3bw53d3eYmJjg0qVLWL58Of766y8EBgbC1tY21evGjx+P48ePo23btvD09MSePXswdepUxMfHY+bMmSn2HTt2LBYsWKCJw97eHo8fP8bRo0dRu3ZtVKlSJdvHnjhxImbPno2SJUuic+fOsLW1xcmTJzF+/HicPXsWO3bsSLHv3LlzUaZMGfTq1QvW1tYIDQ3FqVOncPToUTRt2hRNmzbFw4cPsWHDBnh4eKBp06aa1xcsWBAAEBcXh1atWsHf3x81atTAwIEDkZCQgIMHD6JDhw5YvHgxhg8fnuprNmLECJw5cwZt2rRBu3btYG9vn+b3RFsSEhLQsmVLvH79Gl26dEFMTAy2bduG7t27w9fXFy1btkz3tTVq1MCoUaOwaNEiVK9ePcXPj7ouTJIk9O7dG7///jvKlSuHXr16wdTUFEeOHMHAgQNx48YNzJs3T/O6mJgYNG3aFFevXkX9+vXh4eGBx48f44svvsgwllwnkSRJkhQRESEBkCIiIuQOJdm5c5IESJKpqSQ9fy53NESyiY2NlW7cuCHFxsamflKlkqSoKN2/qVQ5+hoEBwdLACRPT09JkiSpSpUqUuXKlTXPP336VDI2NpZGjBghSZIkmZmZSc7OzimOER4eLr19+zbVsTds2CABkGbMmJFiu5eXlwRAcnV1lZ48eaLZ/vz5c6lgwYKStbW1FBcXp9m+f/9+CYBUtWpV6cWLFymOlZCQIIWFhWX72IcPH9Z8/lFRUZrtKpVKGjx4sARA2rlzp2Z74cKFpRIlSkjR0dGpPt+XL19q7h87dkwCIE2ZMiXVfpIkSd9//70EQJo0aZKkeu97GBkZKbm5uUmmpqZSaGhoqs+rVKlS0qNHj9I8ZlrUcXh5eWV5H2dnZwmA1KFDhxRfs6NHj6b4mVGbMmWKBEA6duyYZpv65yu9869atUoCIPXv31+Kj4/XbI+Li5PatWsnAZAuXLiQ6hyDBg1KcRxfX18JgARA8vHxSfdzVcvwd/8/WXn/5uUtXVanDuDmBsTHA+kMHxIZvJgYwMpK928xMVr9tAcMGIDr16/j7NmzAMRlicTExHQvbQGAvb09rKysUm3v06cPbGxscPTo0TRfN2nSJBQvXlzz2M7ODh06dMDbt29x+/ZtzfZl/zVVXbRoEYoUKZLiGMbGxnBwcMj2sZcsWQIAWLVqFQoUKKDZrlAoMHv2bCgUCvz+++8pjm1qagojI6NU5yxcuHCan+eHVCoVli9fjjJlymguf6lZW1tj8uTJiI+Px65du1K9dvz48XBycsrUebTl119/hampqeZx8+bN4ezsjPPnz+f42EuWLEGBAgWwdOnSFPVipqammhG597/+GzduhKmpKaZPn57iOJ6enmjevHmO48kuXt7SdUOHAgMGiJ4948aJImciMnhffvklvvvuO6xbtw7u7u7w8fFBzZo1UaNGjQxft2vXLqxcuRKBgYF4/fp1ilqYJ0+epPma2rVrp9pWqlQpAMCbN280286dOwczMzN4eHhk+vPI7LHPnDmDAgUKpFs/YmFhgVu3bmke9+jRA8uWLUOVKlXQo0cPNGvWDPXr14eFhUWmY7t9+zZev36NEiVKYNq0aamef/78OQCkOK9aXs+MKliwoKYu532lSpVCQEBAjo4dExODq1evokSJEpgzZ06q5xP+WytS/XWIjIxEcHAwKlWqhGLFiqXav3HjxvDz88tRTNnFpEfXffEF4O0NBAcDf/0FfP653BER6RZLy/zRz0rLM2WKFi2Kdu3aYdu2bejWrRtu376NxYsXZ/ia+fPnY9y4cShatChatmyJUqVKaZKAhQsXIi4uLs3X2djYpNpmbCzePt5PmiIiIlCyZMksTZfP7LFfvXqFxMTENJMPtejoaM39RYsWwdXVFT4+PpgxYwZmzJgBc3NzdO/eHfPnz4ednd1HY3v16hUA4Pr167h+/XqmzquW1qhWRtRfs/QKuN9/Lq2vb1q1WID4WmZ0zMx4/fo1JElCaGhopr7+kZGRAJBuHVNWvzbaxKRH11laAv37A7/+KgqamfQQpaRQAO9d7jAkAwcOxK5du9CvXz+Ym5ujd+/e6e6bmJiIn376CcWLF0dQUFCKNyRJkjB37twcx1OwYEGEhYVBpVJpvU+QjY0NFAoFXrx4kan9jY2NMW7cOIwbNw5PnjzB8ePH4ePjg40bNyIsLAx//fVXps4JAF26dElzFlRG3r8UlhnqpOXly5fp7qP+3NNLcHKL+utQu3ZtXLhwIdP7pzUjEADCw8O1F1wW6fS1kqVLl8LFxQXm5uZwd3fHuXPnMvW6bdu2QaFQpDuDId9R9+w5eBBgy3Yi+o+npydKliyJ0NBQdOzYEYUKFUp33xcvXiAiIgL169dP9R/4hQsXEBsbm+N46tati7i4OBw/fjzHx/qQu7s7Xr58ibt372b5tSVKlEDPnj3h6+uLsmXL4ujRo5rPV13z8+GUdwCoWLEibGxscOHCBc0lnNxSvnx5mJqa4vz58+l221ZfpqpWrZrWz5/R18Ha2hoVK1bEzZs3U1xyTI+NjQ1cXV1x7949hIWFpXr+5MmTOY43u3Q26dm+fTu8vb0xZcoUBAYGonr16vD09Ew3c1R7+PAhxo0bh8aNG+dRpHngk0+Azz4TTQpXrpQ7GiLSEUZGRtizZw92796NWbNmZbivvb09LCwsEBgYiJj3iqpfv36NESNGaCWeYcOGAQBGjRqluTSklpiYmKP/8EeOHAlAFHCnNRoSFhaGmzdvAhDTzP/5559U+0RHRyMqKgomJiaakSh1UfPjx49T7W9sbIwhQ4bg0aNHGDduXJqJz7Vr1z76vpQZ6ktvz58/x4wZM1I9f/XqVaxZswbW1tbo1KlTjs/3oUKFCkGhUKT5dQDE1z8mJgaDBg1K83JecHBwit5Gffr0QXx8PCZPnpxiv8OHD8tWzwPo8OWtBQsWYNCgQejfvz8AYMWKFTh48CDWrVuHCRMmpPmapKQk9O7dG9OmTcPJkyczzEjj4uJSXL9WX4PUWUOGAEeOAGvXAlOnAmZmckdERDrAzc0Nbm5uH91PqVRi6NChmD9/PqpXr4527dohMjISf/75J5ydnVGiRIkcx9K6dWuMGzcO8+bNQ7ly5dCpUyfY29sjNDQUfn5+GDduHEaPHp2tY7dq1QqTJk3CTz/9hLJly6JVq1ZwdnbGy5cvce/ePZw8eRIzZsxAxYoVERsbi4YNG+KTTz5B7dq14eTkhKioKBw4cABhYWEYN24czP77G1qhQgWUKFEC27Ztg5mZGUqVKgWFQoERI0bA1tYW06ZNQ2BgIH777TccPHgQTZo00XxOV69exeXLlxEQEKCVPjzz58/H2bNnMW3aNBw4cAAeHh4wNzfHnTt3sG/fPkiShC1btmh6CGmTlZUV6tSpgxMnTqBPnz4oV64clEol+vTpA2dnZ3zzzTc4c+YMNmzYgNOnT6NFixYoUaIEwsPDcevWLZw9exZbt27V9PX59ttvsWvXLqxevRrXr19HkyZN8PjxY/zxxx9o06YNDh48qPXPIVM+OqldBnFxcZKRkZG0e/fuFNv79u0rtW/fPt3XTZ48WerYsaMkSaJXQocOHdLdV91D4MObTvXpeV9CgiSVLCn69mzZInc0RHkqM7069N2HfXo+Jq0+PfHx8dLMmTOlcuXKSWZmZpKTk5M0duxY6e3bt5Kzs3Oq/dU9Z4KDg1MdP61eL2r/+9//pGbNmkm2traSmZmZ5OLiIvXp00e6du1ajo995MgRqV27dlLRokUlExMTqVixYlL9+vWln376SQoJCdF8nnPmzJFatmwplSpVSjI1NZUcHBykJk2aSFu3bk3Rb0eSJOnMmTOSh4eHZG1trXkveD+uxMREaeXKlVLDhg0lGxsbzdeuVatW0vLly1P0Dcro88qMN2/eSFOmTJGqV68uFShQQDIxMZEcHR2lXr16SYGBgWm+Jq3vnZqHh4f04Vt9el/f27dvS61bt5YKFiwoKRSKNPfZvn271KJFC6lQoUKSiYmJVLJkSalp06bS/Pnzpecf9JN7+fKl9PXXX0tFixaVzM3Npdq1a0u7du2SfHx8ZOvTo5Ak3VvY6cmTJyhZsiT++ecf1H+vE/G3336L48ePa/pSvO/UqVPo0aMHgoKCYGdnh379+uHNmzfYs2dPmudIa6TH0dERERERac4m0Ak//QRMngw0bAicOiV3NER55t27dwgODoarqyvMzc3lDoeI8khmfvcjIyNha2ubqfdvna3pyYq3b9+iT58+WL16daamIQKAmZkZbGxsUtx03ldfAcbGwOnTwJUrckdDRESUr+hkTY+dnR2MjIxSFb2Fh4en2ejo/v37ePjwIdq1a6fZpu5LYGxsjNu3b6NMmTK5G3ReKF4c6NQJ2LFDrL6+fLncEREREeUbOjnSY2pqitq1a6eo8FapVPDz80txuUutQoUKuHr1KoKCgjS39u3bo1mzZggKCoKjo2Nehp+7hg4VHzdtAnS9+JqIiEiH6ORIDwB4e3vDy8sLbm5uqFu3LhYuXIjo6GjNbK6+ffuiZMmSmDVrFszNzVOt3Kuubv9we77n4QFUrAjcvAls3pycBBEREVGGdHKkBwC++OILzJs3D5MnT0aNGjUQFBQEX19fTfvqkJAQPH36VOYoZaBQiOnrgOjQrHt16ERERDpJJ2dvySEr1d+yi4gASpQQqzYfPw40aSJ3RES5irO3iAwTZ28RYGsLfPmluL9smbyxEOUh/o9GZFi0/TvPpCe/Ul/i2rULSGNtEyJ9ol4XKLfXPyIi3aL+nVf/DcgpJj35VY0aQP36QEKCWJqCSI+ZmJjAzMwMERERHO0hMhCSJCEiIgJmZmYwMTHRyjF1dvYWZcLQoUBAgFiEdMIEQEuZMJEusrOzQ2hoKP7991/Y2trCxMQECoVC7rCISMskSUJCQgIiIiIQFRWFkiVLau3YLGT+T74qZFZ79w4oVQp4+RLYuxdo317uiIhyVWRkJF68eJFiCRki0k9mZmaws7P76HtyVt6/OdKTn5mbAwMHAnPnioJmJj2k59RLxiQkJCApKUnucIgolxgZGWntktb7ONLzn3w50gMADx4AZcuKfj1374r7REREBoJT1g1J6dJAq1bi/sqV8sZCRESkw5j06AP1UhTr1gGxsfLGQkREpKOY9OiDzz8HnJ2BV6+AP/6QOxoiIiKdxKRHHxgZAd98I+4vXy5vLERERDqKSY++GDgQMDEBzp4FLl6UOxoiIiKdw6RHX9jbA926ifsc7SEiIkqFSY8+URc0b90KvH4tbyxEREQ6hkmPPmnQAKhaVczg2rhR7miIiIh0CpMefaJQJI/2LFsmGhYSERERACY9+qd3b8DaGrhzB/j7b7mjISIi0hlMevSNtTXQp4+4z4JmIiIiDSY9+mjIEPFxzx4gNFTWUIiIiHQFkx59VKUK0KQJkJQErF4tdzREREQ6gUmPvlKP9qxeDSQkyBsLERGRDmDSo686dxYNC588AfbtkzsaIiIi2THp0VempsCgQeL+smXyxkJERKQDmPTos6+/BpRKMXX91i25oyEiIpIVkx595uQEtG0r7q9YIW8sREREMmPSo+/UHZrXrweio2UNhYiISE5MevTdZ58BZcoAERHA77/LHQ0REZFsmPToO6USGDxY3Od6XEREZMCY9BiC/v0BMzPg0iXg3Dm5oyEiIpIFkx5DUKQI0KOHuM/p60REZKCY9BgKdYfm7duBly/ljYWIiEgGTHoMRd26QK1aQFwc4OMjdzRERER5jkmPoVAokqevr1gBqFTyxkNERJTHmPQYkh49AFtb4P594MgRuaMhIiLKU0x6DEmBAkC/fuI+C5qJiMjAMOkxNOqC5gMHgJAQeWMhIiLKQ0x6DE358kDz5qKmZ9UquaMhIiLKM0x6DJF6tGf1aiA+Xt5YiIiI8giTHkPUvj1QogTw7Bmwa5fc0RAREeUJJj2GyMQE+PprcZ8FzUREZCCY9Biqr74CjIyAkyeBa9fkjoaIiCjXMekxVCVLAh07ivvLl8saChERUV5g0mPI1B2aN24E3r6VNxYiIqJcxqTHkDVrJqawR0UBW7bIHQ0REVGuYtJjyBSK5Onry5YBkiRvPERERLmISY+h8/ICLCyAq1eB06fljoaIiCjXMOkxdAULAr17i/ssaCYiIj3GpIeSL3Ht2CEaFhIREekhJj0E1KoFuLsDCQnA2rVyR0NERJQrmPSQoJ6+vnIlkJQkbyxERES5gEkPCd27A4ULA48eAX/+KXc0REREWsekhwRzc2DAAHGf63EREZEeYtJDyQYPFh99fYEHD+SNhYiISMuY9FCyMmUAT0/RpHDlSrmjISIi0iomPZSSuqB57Vrg3Tt5YyEiItIiJj2UUps2gJMT8PKl6NtDRESkJ5j0UEpGRsDXX4v77NBMRER6hEkPpTZwIGBiAgQEAJcuyR0NERGRVjDpodSKFQO6dBH3OdpDRER6gkkPpU1d0LxlCxARIW8sREREWsCkh9LWqBFQuTIQEwNs3Ch3NERERDnGpIfSplAkj/YsWyZ69xAREeVjOUp6Xr9+ra040rR06VK4uLjA3Nwc7u7uOHfuXLr77tq1C25ubihYsCAKFCiAGjVqYNOmTbkan9778kvAygq4dQvw95c7GiIiohzJUdJTqlQpDBo0CEFBQVoKJ9n27dvh7e2NKVOmIDAwENWrV4enpyeePXuW5v6FCxfGDz/8gICAAFy5cgX9+/dH//798ddff2k9NoNhYyMSH4AFzURElO8pJCn71y1MTEyQlJQEhUKBBg0aYPjw4ejSpQuMjY1zHJi7uzvq1KmDJUuWAABUKhUcHR0xYsQITJgwIVPHqFWrFtq0aYOffvop1XNxcXGIi4vTPI6MjISjoyMiIiJgY2OT4/j1xpUrQPXqgLGxWIG9RAm5IyIiItKIjIyEra1tpt6/czTSExISgkmTJsHBwQGnT59Gr1694OTkhGnTpiEsLCzbx42Pj8fFixfRokWL5ECVSrRo0QIBAQEffb0kSfDz88Pt27fRpEmTNPeZNWsWbG1tNTdHR8dsx6vXqlUTRc2JicCaNXJHQ0RElG05SnqKFy+OadOmISQkBFu3bkWDBg0QFhaG6dOnw9nZGT179sSpU6eyfNwXL14gKSkJDg4OKbY7ODhkmExFRETAysoKpqamaNOmDRYvXozPPvsszX0nTpyIiIgIze3x48dZjtNgDBkiPq5aJZIfIiKifEgrs7eMjY3Ro0cPnDx5EpcvX8ZXX30FU1NTbN++HR4eHqhZsybWrl2Ld7m8gKW1tTWCgoJw/vx5zJw5E97e3vBPpwDXzMwMNjY2KW6Uji5dgKJFgdBQYP9+uaMhIiLKFq1PWa9atSpWrlyJf//9F+PGjYMkSbhy5Qq+/vprlCxZEpMmTUJkZGSGx7Czs4ORkRHCw8NTbA8PD0exYsXSfZ1SqUTZsmVRo0YNjB07Fl27dsWsWbO08nkZNDMz4KuvxP2lS+WNhYiIKJtypU/PyZMn8fXXX2PRokUAAFNTU9StWxdv3rzBzz//jEqVKuH69evpvt7U1BS1a9eGn5+fZptKpYKfnx/q16+f6ThUKlWKYmXKgW++AZRKwM8PuHZN7miIiIiyTGtJT2xsLFatWoXq1aujadOm2LFjB+zs7DB9+nSEhIQgICAAt27dQrdu3fDkyROMHTs2w+N5e3tj9erV2LBhA27evIkhQ4YgOjoa/fv3BwD07dsXEydO1Ow/a9YsHDlyBA8ePMDNmzcxf/58bNq0CV+qp1xTzjg7A507i/sLFsgbCxERUTbkeG75vXv3sHTpUmzYsAERERGQJAl169bFyJEj0b179xTT18uVK4dt27bh0aNHOHPmTIbH/eKLL/D8+XNMnjwZYWFhqFGjBnx9fTXFzSEhIVAqk3O26OhoDB06FP/++y8sLCxQoUIFbN68GV988UVOP0VSGzcO2LkT2LwZmDkTKF5c7oiIiIgyLUd9ej7//HMcOXIEKpUKJiYm6Nq1K0aOHAl3d/cMXzdw4ECsX78eSUlJ2T211mVlnr9Ba9QIOH0a+P57kfgQERHJKCvv3zka6fnrr79QtGhRfP311xg6dCiKZ/I//44dO8LJySknpya5jB0rkp7ly0XiU6CA3BERERFlSo5GetavX49evXrB1NRUmzHJgiM9mZSUBFSoANy7ByxeDAwfLndERERkwPKsI3Pp0qXx8OHDj+539+5dnDhxIienIl1hZASMGSPu//qrSIKIiIjygRwlPc2aNcOcOXM+ut/cuXPRrFmznJyKdEm/fkCRIsCDB8CePXJHQ0RElCk5SnokSUIOro5RfmVpmbw0xbx58sZCRESUSbnSnPBDr1+/hrm5eV6civLK8OGAqSlw5gzwzz9yR0NERPRRWZ69FRISkuJxVFRUqm1qiYmJuH79Og4fPowyZcpkL0LSTQ4OQJ8+wNq1wPz5QIMGckdERESUoSzP3lIqlVAoFADE5S31/YxIkoTZs2fj22+/zV6UeYCzt7Lhxg2gcmVAoQDu3AHKlpU7IiIiMjC52qfHyclJk+iEhITA0tISdnZ2ae5ramqKUqVKoUuXLhiirgEh/VGpEtC6NXDoELBwIbBkidwRERERpStHfXqUSiX69euHdevWaTMmWXCkJ5uOHQM+/RSwsAAePxazuoiIiPJInvXp8fHxwcCBA3NyCMrvmjYFatYEYmOBFSvkjoaIiChdORrp0Scc6cmBrVuB3r1FcfPDhwBn6hERUR7Js5EeIgBAt25AqVJAeLhIgIiIiHRQlgqZS5cuDYVCgaNHj8LV1RWlS5fO9GsVCgXu37+f5QApHzAxAUaPBsaNE9PX+/cXM7qIiIh0SJYub6mnq9+8eROffPIJlMrMDxQpFAok6fA6Tby8lUMREYCjI/D2rZjN9fnnckdEREQGINemrAcHBwMASpYsmeIxEWxtgUGDgAULxNIUTHqIiEjHsJD5Pxzp0YKQEKB0abHyemCgmNVFRESUi1jITPJwcgK6dxf358+XNxYiIqIPMOkh7Ro7Vnzcvl00KyQiItIRWarpGTBgQLZPpFAosHbt2my/nvKJ2rVFw0J/f+C334BffpE7IiIiIgDZmL2V7RNx9pbhOHgQaNsWsLERoz38ehIRUS7JtdlbPj4+OQqMDMTnnwMVKgC3bgFr1gDe3nJHRERExNlbahzp0bI1a8QUdicn4N490cCQiIhIyzh7i+T35ZeAvb2Yxr5zp9zREBERMemhXGJuDgwfLu7Pnw9wQJGIiGSWpctbGzduBAB06tQJ1tbWmseZ1bdv36xFl4d4eSsXvHghLm/FxorZXB4eckdERER6Jivv3zlee0uRhYUlOXvLAA0dCixfLmZz7d8vdzRERKRncm32Vt++faFQKGBra5viMVG6xowBVqwADhwQs7kqVJA7IiIiMlCcvfUfjvTkok6dgD17xGyuVavkjoaIiPQIZ2+RblEvTbFxI/DsmbyxEBGRwWLSQ7mvYUPA3R2IiwOWLpU7GiIiMlBaSXpu3LiBwYMHo0KFCrCyskKBAgVQvnx5DB48GNeuXdPGKSg/UyiSR3uWLQNiYuSNh4iIDFKOa3qWLl0Kb29vJCYmIq1DmZiY4JdffsHIkSNzcppcx5qeXJaYCJQrBzx8KGZzDR4sd0RERKQH8qym588//8SIESOQmJiIzp07Y9++fbh69SquXr2K/fv3o2vXrkhKSsKYMWPw559/5uRUlN8ZG4uZXACwYAGgUskbDxERGZwcjfQ0a9YMJ06cwLZt29CtW7c099m5cye6d+8ODw8PHDt2LNuB5jaO9OSBqCjA0RF480bM5urQQe6IiIgon8uzkZ6LFy+ibt266SY8ANC1a1e4u7vj4sWLOTkV6QMrq+TLWvPnyxsLEREZnBwlPQqFAmXKlPnofmXKlGETQxJGjBArrp88CZw7J3c0RERkQHKU9FSrVg1379796H53795F1apVc3Iq0hclSgC9eon7HO0hIqI8lKOkx9vbG+fPn8e2bdvS3Wf79u04f/48xqiLWIm8vcXHnTuB4GB5YyEiIoORpbW3QkJCUjyuXbs2xowZgy+//BI7d+5E37594erqCgAIDg7Gpk2bsHv3bowZMwZ16tTRXtSUv1WrBrRsCRw+DCxaBCxcKHdERERkALK1yvqHJElKt2ZH/ZxCoUBiYmL2I81lnL2Vxw4fBjw9gQIFgMePgUKF5I6IiIjyoVxbZd3JyYkFyaQdn30GVK0KXL0qFiH97ju5IyIiIj3HVdb/w5EeGWzYAPTrJ4qbg4MBU1O5IyIionyGq6xT/tCzp0h4njwBMiiGJyIi0gYmPSQfU1PRtwcQ09c56EhERLlIq5e3IiIiEBkZmebCo4CoCdJVvLwlk9evxdIU0dGiuPmzz+SOiIiI8pFcK2ROy+vXrzF58mTs2LEDz58/T3c/XZ+9RTIpVAgYOBD47Tcx2sOkh4iIckmOLm9FRESgXr16WLZsGV69egULCwtIkoRixYoBgGbEx8nJCY6OjjmPlvTT6NGAUgn89ZeYzUVERJQLcpT0/PLLL7h79y769u2LiIgIdO3aFQqFAqGhoXj79i2WL1+OggULwsPDA8HsvEvpcXUFunQR9xcskDcWIiLSWzlKevbt2wc7OzssX74cFhYWKXr4WFpa4ptvvsHBgwexefNmrFq1KsfBkh4bO1Z83LJFzOYiIiLSshwlPQ8ePEDt2rVhbm4OAJqkJykpSbNPvXr1UL9+faxduzYnpyJ95+4ONGoEJCQAS5bIHQ0REemhHE9ZL/Te8gGWlpYARHHz+5ycnHDr1q2cnor0nXq0Z/lyICpK3liIiEjv5CjpKVGiBEJDQzWP1VPSr1y5kmK/Bw8ewNg4xxPFSN+1aweUKwe8eQP4+MgdDRER6ZkcJT1Vq1bF7du3NY8bN24MSZIwZcoUvH37FgCwefNmnD17FpUqVcpZpKT/jIyAMWPE/V9/Bd67TEpERJRTOUp6WrVqhWfPnuHYsWMAgPr166Nhw4Y4ffo0ChcujCJFisDLywsKhQLffvutVgImPeflBRQpItbi2r1b7miIiEiP5Cjp6dmzJ06ePIlPPvlEs23Xrl1o27YtAFHbU7BgQSxYsADt2rXLWaRkGCwtgaFDxf1587g0BRERaU2urbIeExODiIgIODg4QKnU/SW+uAyFDgkPB5ydgbg44NQpoGFDuSMiIiIdpROrrFtaWqJ48eL5IuEhHePgAPTpI+7PmydvLEREpDe0mpGEhYXhwoULOH/+PJ4+farNQ5Oh8fYWH/fuBe7elTcWIiLSC1pJelavXo0KFSqgZMmScHd3R7169VCqVClUqFABK1eu1MYpyNBUrAi0aSNqen79Ve5oiIhID+SopkelUqFnz57YuXOnZnHRIkWKAABevnwpTqBQoHPnzti+fbtOX+piTY8O8vcHmjUDLCyAkBDAzk7uiIiISMfkWU3PkiVLsGPHDtjZ2WHx4sWIjIzE8+fP8fz5c0RGRmLJkiWwt7fHrl27sIRLC1BWeXgAtWoBsbGiSzMREVEO5CjpWbt2LczMzODv749hw4bByspK85yVlRWGDh2Kv//+GyYmJlizZk2Wj7906VK4uLjA3Nwc7u7uOHfuXLr7rl69Go0bN0ahQoVQqFAhtGjRIsP9KR9QKIBx48T9JUuAd+/kjYeIiPK1HCU9d+/eRdOmTVGxYsV096lYsSKaNWuGe/fuZenY27dvh7e3N6ZMmYLAwEBUr14dnp6eePbsWZr7+/v7o2fPnjh27BgCAgLg6OiIli1bplgmg/Khrl0BR0fg2TOxAjsREVE25SjpsbKySrHgaHoKFSqUYhQoMxYsWIBBgwahf//+qFSpElasWAFLS0usW7cuzf23bNmCoUOHokaNGqhQoQLWrFkDlUoFPz+/NPePi4tDZGRkihvpIBMTYNQocX/+fEClkjceIiLKt3KU9DRq1Ahnz56FKoM3IpVKhbNnz6JBgwaZPm58fDwuXryIFi1aJAeqVKJFixYICAjI1DFiYmKQkJCAwoULp/n8rFmzYGtrq7k5OjpmOj7KY4MGATY2wM2bgK+v3NEQEVE+laOkZ+rUqXj69ClGjx6N+Pj4VM8nJCRg9OjRCAsLw7Rp0zJ93BcvXiApKQkODg4ptjs4OCAsLCxTx/juu+9QokSJFInT+yZOnIiIiAjN7fHjx5mOj/KYjY1IfAA2KyQiomwzzsrOGzduTLWtf//+WLp0KXbt2oXu3bvD1dUVABAcHIwdO3bgyZMnGDx4MC5fvozq1atrJ+qPmD17NrZt2wZ/f3+Ym5unuY+ZmRnMzMzyJB7SglGjgEWLgGPHgMBAMauLiIgoC7LUp0epVEKhUKTarj7Eh899uD0pKSlT54mPj4elpSV27tyJjh07arZ7eXnhzZs32Lt3b7qvnTdvHmbMmIGjR4/Czc0tU+cD2KcnX+jdG9i6FejVi0XNREQEIGvv31ka6enbt2+aSY+2mZqaonbt2vDz89MkPeqi5OHDh6f7urlz52LmzJn466+/spTwUD4xdqxIerZvB2bPFrO6iIiIMilLSc/69etzKYzUvL294eXlBTc3N9StWxcLFy5EdHQ0+vfvD0AkYCVLlsSsWbMAAHPmzMHkyZOxdetWuLi4aGp/rKyssjxzjHRUrVqiQ/OxY+JSF+t7iIgoC3R2XYgvvvgC8+bNw+TJk1GjRg0EBQXB19dXU9wcEhKSYlHT5cuXIz4+Hl27dkXx4sU1t3l8Y9Qv6maFq1YBERHyxkJERPlKjtbe+pAkSZo1twoXLqzTa219iDU9+YRKBVSpIqavz5snLnkREZHByrO1t9T8/PzQqlUrWFlZwcHBAQ4ODrC2tsbnn3+ebnNAomxRKpMTnUWLgIQEeeMhIqJ8I8dJz/Tp09GyZUscPnwYsbGxkCQJkiQhNjYWf/31F1q2bIkZM2ZoI1YioXdvwN4eePwY2LFD7miIiCifyFHSc/ToUUydOhUmJiYYPnw4Ll26pFnSISgoCCNGjICpqSmmTJmCv//+W1sxk6EzNwdGjBD3588HtHeFloiI9FiOanrat2+PgwcP4tChQ/D09Exzn8OHD+Pzzz9H27ZtM+yvIzfW9OQzL1+KKeuxscDff4tZXUREZHDyrKZHvaZWegkPALRs2RINGjTI9JpZRJlSpAjwX/sCzJ8vbyxERJQv5CjpefPmDZydnT+6n7OzMyI4vZi0bcwYQKEADh4Us7mIiIgykKOkx87ODrdu3frofrdu3YKdnV1OTkWUWtmygHqZkgULZA2FiIh0X46SnoYNG+LSpUvYunVruvts2bIFgYGBaNSoUU5ORZQ29fT1jRuB8HB5YyEiIp2Wo6Rn/PjxUCgU6Nu3L7p3746DBw/ixo0buHHjBg4cOICuXbvCy8sLRkZGGKfupEukTQ0aAO7uQHw8sHSp3NEQEZEOy3FH5tWrV2PYsGFITExMc5V1Y2NjLF26FIMGDcpRoLmNs7fysZ07gW7dRHFzSAhgaSl3RERElEfytCPzoEGDEBgYiAEDBqB06dIwMzODmZkZSpcujYEDByIwMFDnEx7K5zp1AlxdxTT2DRvkjoaIiHRUjkZ6QkJCoFAo4OjoqM2YZMGRnnxu8WJg5EigXDkxk8vISO6IiIgoD+TZSI+Liwt69OiRk0MQaUf//kDBgsDdu8D+/XJHQ0REOihHSY+NjQ1cXV21FQtR9llZAUOGiPtsVkhERGnIUdJTqVIlPH78WFuxEOXM8OGAiQlw6hRw9qzc0RARkY4xzsmLBw0ahEGDBuH8+fOoU6eOtmIiyp4SJcQK7OvXi9GeP/6QO6Jck5QE+PoC164BpqaAmVnmb2ntr8zxlAYiIt2X4ynrI0eOxKZNmzB+/Hh06dIFLi4uMDMz01Z8eYaFzHri6lWgWjXxLn7vnpjVpUfCwoA1a4BVqwBtDrIaG2cvWdLWa4oUAQoV0t7nQ0SGIyvv3zlKeoyyMENGoVAgMTExu6fKdUx69EirVsBff4nZXIsWyR1NjkkS4O8PLF8O7N4NqH+NihQRn6okAXFxmb/Fx4uPukShAJo0Ee2WunQBihWTOyIiyi/yLOlRZnFMXKVSZfdUuY5Jjx45cgRo2RIoUEAMh+TTIYTXr0XboRUrgNu3k7c3bChqtrt0AczNs3dsSQISErKWLH2YNGX3ltbr375Njk2dAHXvDnTuzASIiDKWZ0mPPmHSo0ckCahRA7hyBZg1C5gwQe6IsuT8eTGqs20bEBsrtllZAX36AIMHi6t3+ubRI9FYe8eOlDXoCgXg4ZE8AuTgIF+MRKSbcj3puXfvHnbt2oWHDx/CzMwMNWvWRLdu3WBhYZHtoOXGpEfPbNwIeHkBxYsDDx+K4hIdFhMD/P67SHYuXkzeXq2aGNXp3RuwtpYvvryUXgKkVKYcAWICRERALic9CxcuxLfffoukpKQU20uWLIlDhw6hSpUqWY9YBzDp0TPx8aKI+ckTMZvLy0vuiNJ086a4fLVhAxARIbaZmYmRjSFDgPr1xWiHoVInQH/8AZw7l7xdqUweAWICRGTYci3pOXXqFDw8PCBJEgoUKIDy5csjMjISDx48gEqlQrly5XDz5s0s1/roAiY9emjOHHFpq2pV4PJlncke4uNFQfKKFaJAWa1MGeCbb0RzaTs72cLTWQ8fJo8ApZUAqUeA7O1lC5GIZJBrSU+PHj3wxx9/wMvLC0uWLEGBAgUAAFeuXEGXLl3w4MED7N+/H61bt87ZZyADJj166M0bwNERiIoSs7latpQ1nEePxFTztWuB8HCxTakE2rcXozotWrBfTmapE6A//hA1UGpKJdC0afIIEBMgIv2Xa0mPs7MzJEnCvXv3YPpBjcShQ4fQtm1b/Pjjj5g+fXr2IpcRkx49NXq0mLb+2WfA4cN5fvqkJJFvLV8OHDoEqCcwFi8ODBokbqVK5XlYeiU4OHkEKK0ESD0CVLSobCESUS7KtQVHw8PD4ebmlirhAYBGjRoBAJ49e5aVQxLlrlGjxLvfkSNiNlceefYMmD0bKFsWaNMGOHBAJDzNm4s36EePgGnTmPBog6srMH68uOT14AEwdy7g5ia+3n//LWa8FSsmRtJWrgSeP5c7YiKSS5aSnvj4eBQsWDDN59TZVXx8fI6DItIaV1ega1dxP5cXIpUk4MQJoFcvkcxMnCguwxQqBIwZI3rtHD0qpl6bmORqKAZLnQCdPy8SoDlzkhMgPz8mQESGjhUEpP/GjhUff/9dzObSsogIYMkSUS/t4SFOk5AA1K0L+PgAoaHAggXAJ59o/dSUAVdX4NtvRQJ0/75IgGrXTpkAFS8uEqBVq5gAERmCLNX0KJVKNGrUCF999VWaz/fr1y/D5/v27Zu9KPMAa3r0XJMmwMmTYjbXrFlaOeSlS6JWZ+tWIDpabLO0FD11Bg8GatXSymlIyx48EPU/O3ak7IlkZAQ0ayaKoDt1Yg0QUX6Ra4XMSqUSimxO++XaWySrvXuBjh2BggXF0hRWVtk6TGysmDG0fHnKxnmVKokZWH36ALa2WomY8oA6AfrjDyAwMHm7OgHq3l0kQGwhQKS7ci3pcXFxyXbSAwDBwcHZfm1uY9Kj51QqoEIF4O5dMZtr5MgsvfzOHVED4uMj1sQCRF1Oly4i2WncWGfaAFE23b+fPAL0YQL06afJI0BMgIh0C9feygYmPQZgxQqRobi4iOTH2DjD3RMSgH37xKiOn1/ydmdn0URwwAB2AtZXH0uA1CNARYrIFyMRCUx6soFJjwGIiREZy4sX4npGt25p7vbvv8Dq1cCaNcl1zwoF0Lq1yJlatRJvfmQY7t1LboR46VLydiMj0YJAPQLEBIhIHkx6soFJj4GYMgWYPh2oUwc4c0bTAlmlEtPJly8H9u8XTQUB0dH3q69EE0EXF/nCJt1w717yCFBaCdAXXwA9eoiCdiLKG0x6soFJj4F49kyM9rx7B3z/PV56z4SPj7jydf9+8m4eHmJUp1MnnV+gnWSiToD++AMICkreXrQoMGIEMHQoR3+I8gKTnmxg0mM4pA0boegnVl3/2ngdVif2BwDY2IjF2AcPFrOxiDLr7l2RAK1eLRpSAmK0Z9Ag0ZjS2VnW8Ij0GpOebGDSYxhCQkTHZM/TkzAJM5AAYwwvdxh1vm2Gnj2B/9bQJcqWxERR/zNnTvLoj5ER0LOn6BRdrZqs4RHpJSY92cCkR/8dPSrqLV6+BCzMVDhWohfcg7dDKlQIioAAoHx5uUMkPSFJ4udt7lzxUa1VK+C778TlU7Y4INKOXFtwlCg/UqlEE2ZPT5Hw1KoF3LilhPt1H6BePShevxargr54IXeopCcUCuCzz8Q6txcuiAJnpRLw9RVND93dgf/9L7lgnojyBpMe0msREUDnzsD334vkZ8AA4PTp/2ZiWVgAe/aIB/fvix3j4uQNmPRO7drAtm2iweXQoYC5uVgPrGtXoGJFse7Xu3dyR0lkGJj0kN66dk3MTN+7V8zAWrUKWLtWvOloODgABw6IKuaTJ0XlKa/4Ui4oUwZYuhR49AiYNAkoVEgUQH/zjci7f/45uds3EeUOJj2kl37/XVxCuHsXcHQETp0S+UyaKlcWU2+MjIBNm4CZM/M0VjIs9vaiVVRICLBwIeDkBISHAz/8IO6PHSsaZBKR9jHpIb2SkACMHi1maMXEAC1aiGUE6tT5yAtbthT/hgPi3/Bt23I7VDJwVlbAqFGi38+mTUDVqkBUFLBgAeDqCvTrB1y/LneURPqFSQ/pjadPRZHookXi8cSJonA00wtEfvMN4O0t7vfrBwQE5EaYRCmYmABffglcvgwcOgQ0bSqmvm/YAFSpArRrJ0YqedWVKOeY9JBeOHlSzMo6fVqU5+zZI2oksrxG1ty5QIcOoqC5QwfgwYPcCJcoFYUC+Pxz4Ngx4OxZoEsXse3AAaBxY6BhQ/FzrVLJHSlR/sWkh/I1SRIjO59+CoSFifKc8+dFvpItRkbAli1AzZrA8+dA27bAmzfaDJnoo+rWFU0Ob98Gvv4aMDMTA4+dOolu4WvXcqIhUXYw6aF8KypK1O6MHi0uB/TsKf5D/uSTHB64QAGx6mjJksDNm2IZ7YQEbYRMlCXlygErV4qlLSZOBGxtRSL01Vei7mfuXNGWgYgyh0kP5Ut37gD16ol6Y2NjMdqzZYsWl5EoWVIkPgUKiJa6w4axqIJkU6yYuFz7+DEwb5748Xz6VHR3dnISH588kTtKIt3HpIfynT17ADc3MbOlWDFRAzFyZC609a9ZU8x9VyjESpILFmj5BERZY20tprQ/eAD4+IhLXZGRYsTH1VWMAN26JXeURLqLSQ/lG0lJYoi/Uyfg7VtR3BkYCDRqlIsnbdcuOdkZP15kXEQyMzUVEwyvXhUDko0aAfHxotanUiXxO8LJh0SpMemhfOH5c7FY4+zZ4vHo0YCfH1C8eB6cfNQoYMgQcXmrd2/g4sU8OCnRxymVotb+5Ekxc7FDB/FjumcP0KCB+MfgwAHO+CJSY9JDOu/cObF+0dGjgKWluOL066+iv0meUCiA334TK5bGxIjRH7bMJR3ToIFIdm7eFGvMmZiI/j7t2gHVqom+P/HxckdJJC8mPaSzJEmsl9W4sSjgLFdOJEA9esgQjLEx8Mcfolvc06fi3+uoKBkCIcpYhQriMtfDh8C334q+Vdevi8thZcqIq7Vv38odJZE8mPSQToqNBQYOFE2S4+OBjh1F/53KlWUMysZGXCuwtxftc3v2FIVGRDqoRAlgzhyxxtecOeJS8L//ikJoR0fg++/Fml9EhoRJD+mc4GDRfdbHR9QszJ4N7NolepTIztkZ2LdPLNV+4IB4ByHSYba2YsQnOBhYswYoX1709pk1S/w4f/ONWJiXyBAw6SGd4usr6ncuXRJrZh0+LHqQaH06ek64uwMbN4r7ixYlL1RKpMPMzMTo6Y0bwO7dos9VXJy4hFy+PNC1qxhNJdJnTHpIJ6hUwE8/Aa1bA69fi1XRL14EmjeXO7J0dOsmusUBokmQr6+88RBlklIpLhf/8w9w4oQoT5Mk4H//E8tfNGsG/Pkne3GSfmLSQ7J7/Rpo3x6YPFn8of3mGzEF18lJ7sg+YsIEUR2qUgHdu4umKUT5hEIhJgns3y9+dL28RL2+v7/454MzvkgfMekhWV2+LLorHzwoht/XrQNWrBD3dZ5CIRZG8vAQ02HathWrnhLlM1WqAOvXi07PY8YAVlbAtWsipy9dGvjlF67xRfqBSQ/JZtMmoH598YfWxUUMt/fvL3dUWWRqKqqsP/lETJPp0EH08iHKhxwdxZT2kBBR6Fy8OBAaKgqhHR2BceNE+wii/IpJD+W5+HixfmffvmJqeqtWwIULQK1ackeWTYULi6GqwoVFIyEvL7bApXytUCFx9TY4WIy+VqokBjPnzxcjP336iFFaovxGZ5OepUuXwsXFBebm5nB3d8e5c+fS3ff69evo0qULXFxcoFAosHDhwrwLlLIkNFRcDVq2TDyePFnM/C5SRN64cqxsWdEO18QE2LkT+PFHuSMiyjEzMzH6evWqyOubNgUSE4HNm4EaNYCWLYEjR1j0TPmHTiY927dvh7e3N6ZMmYLAwEBUr14dnp6eePbsWZr7x8TEoHTp0pg9ezaKFSuWx9FSZvn7i9GcM2eAggVFAeW0aYCRkdyRaUnjxqIVLiCuDfj4yBsPkZYolaK4+dgxMa39iy/EtiNHROJTs6ZIhBIS5I6UKGMKSdK9HN3d3R116tTBkiVLAAAqlQqOjo4YMWIEJkyYkOFrXVxcMHr0aIwePTpL54yMjIStrS0iIiJgY2OT3dApDZIkhsUnTBANjKtXF9Njy5SRO7JcMnmymH9vbCwaDTVrJndERFoXHAwsXCgaHqrL2EqVEosBDxokGpgT5YWsvH/r3EhPfHw8Ll68iBYtWmi2KZVKtGjRAgEBAVo7T1xcHCIjI1PcSPvevhWzucePFwlPnz6iYFlvEx5ADF/16CGuA3TuDNy+LXdERFrn6ip6cz5+DMycCTg4iGUuxo0TRc/ffScuZxPpEp1Lel68eIGkpCQ4ODik2O7g4IAwLU4HnjVrFmxtbTU3R0dHrR2bhJs3RbOznTtFqcvSpaLvh6Wl3JHlMoVCXNqqXx948wZo0wZ48ULuqIhyReHCYh2vhw+B1avFgqeRkcDcuSIx6tePLaxId+hc0pNXJk6ciIiICM3tMedhatXOnSLhuXVLLHx4/DgwdKiOLSeRm8zNRWGziwtw/z7QqZPo+U+kp8zNga++Eiu679sHNGkianw2bBCNDj//HPj7bxY9k7x0Lumxs7ODkZERwj9Y/jc8PFyrRcpmZmawsbFJcaOcS0wUl7K6dQOiosRsj8BAMehhcOztxZQXW1vg1CnxjsC/+KTnlEqgXTvxj86ZM2JNL6VSrNTSvLloRvr77+JvBVFe07mkx9TUFLVr14afn59mm0qlgp+fH+ob5Dtn/hEeDnz2GTBvnng8fryY3fHBlUrDUqmSGPYyMhLTW2bMkDsiojzj7g7s2AHcuSN6c1lYiH+CevUSXR4WLRL/HBHlFZ1LegDA29sbq1evxoYNG3Dz5k0MGTIE0dHR6P9fu96+ffti4sSJmv3j4+MRFBSEoKAgxMfHIzQ0FEFBQbh3755cn4LBCQgQq6P7+4sW9jt2iGv6xsZyR6YDWrQAli8X9ydPFv/mEhmQMmWAJUtEp+fp04GiRYFHj8RML0dHURP09KncUZJBkHTU4sWLJScnJ8nU1FSqW7eudObMGc1zHh4ekpeXl+ZxcHCwBCDVzcPDI9Pni4iIkABIERERWvws9J9KJUlLl0qSiYkkAZJUoYIk3bghd1Q6atw48UUyM5Ok06fljoZINjExkrRihSSVKyd+JQBJMjWVpAEDJOn6dbmjo/wmK+/fOtmnRw7s05N1MTHA4MFiDS1AXLtftw6wtpY3Lp2VlCS+SHv2AHZ2wNmzoqc/kYFSqUTR8y+/iFYWam3aiMvjTZoY0OQHyrZ83aeH8of790Vx8qZNolxl3jzgjz+Y8GRIXddTq5aYwt6mjZjSTmSglEqgY0fg9Glx69RJJDnqJS/c3cXfFRY9k7Yw6aEsO3BA1O9cuSImKB09Cowdy//IMqVAAbH+RsmSYj5/167s3U8EoEEDYNcu0ctz8GAxBV695MUnnwCLFwPR0XJHSfkdkx7KtKQkYMoUMR01IkKM9AQGiv/IKAtKlBCZY4ECgJ+faGDEq8xEAIBy5UTd/6NH4u9NkSJiyYuRI0XR848/ipmiRNnBpIcy5fVroG1bMfMCENNP/f3FgAVlQ40awLZtYnx/zRqxOBkRadjbA1Onihlfy5aJGWCvX4slL5ydga+/FoOlRFnBpIc+6sYN0V3Z11f02di4UUw/NTWVO7J8rm1b4Ndfxf1vvwV275Y3HiIdZGkJDBkiLnvt3CnqfOLixJIXFSsCHTqI3p8cLKXMYNJDGdq/H6hXD7h3D3ByEsWGffrIHZUeGTFCDJtJEtC7N3DxotwREekkIyOgSxfRE+zkSaB9e7F93z6gcWNxuf1//xOX4YnSw6SH0iRJYhi5QwexUrqHB3DhAlCzptyR6RmFAli4EGjVCoiNFQVTXAeOKF0KBdCoEbB3r7i8NWgQYGYmOkB07QqULy8uh8XEyB0p6SImPZRKdLSYMfHjjyL5GTZMLCdRtKjckekpY2Ng+3agShXRlrZdO5FpElGGypcHVq0SRc8//ihWfL9/X/zNcnIShdChoXJHSbqESQ+lEBwspo7u2AGYmIg/KEuWiPuUi2xsxIwuBwfg8mWgZ082JyHKJAcH4KefRNHzb78BLi7Ay5di4oWTk1jh/Y8/gHfv5I6U5MakhzSOHQPq1Enuv3PsmBg6pjzi7CwKFMzNRXe2sWPljogoXylQQJTJ3b0rBk8bNRJdn319xeh1iRJiFOjCBRY+GyomPQRJEqM5n30m/juqXVv8UWjYUO7IDFDdusnrevz2m/jGEFGWGBsD3buLguc7d4AffgBKlRJT3pctE//cVasGLFjAnj+Ghmtv/cdQ196KixP/+axdKx737i2mglpYyBuXwZs9G5g4UfTx2b8faN1a7oiI8rWkJNELdP160fk5Lk5sNzYWv179+4uPbMWR/2Tl/ZtJz38MMekJCwM6dxZTQJVKYM4cLiehMyQJ+OorsYKrlZXoFVCtmtxREemFN29Eb1AfH+DcueTtdnbAl1+KBIi/bvkHk55sMLSk5/x5sbhfaChgayv+ALRqJXdUlEJ8vPimHDsm+u+fOwcUKyZ3VER65cYNMfqzaZP4R1CtVi2gXz+gVy+xFAbpLiY92WBISc+mTaJAOS5OdDTdu1esd0M66PVr0XXt9m1RiODvL1rUEpFWJSYCf/0lRn/27UteB9jUVDRC7NcP8PQUl8NIt2Tl/ZuFzAYkMREYNw7o21ckPO3aAWfOMOHRaYUKiansRYqI4bm+fcV0FCLSKmNjoE0bsdTFkydiHkHNmmLAdedOsWqMkxPw3XfAzZtyR0vZxaTHQLx+LX6h1eta/vgjsGePaA9DOq5sWbEul6mp6LP/ww9yR0Sk1+zsxNT3wEAgKAgYNUpse/oUmDsXqFRJLM+zcqWoD6L8g5e3/qPPl7du3BDLSdy7J66MrF8PdOsmd1SUZZs3Jy98tnYtMGCAvPEQGZD4eNE+y8cHOHQoeY0vc3NRH9m/P/Dpp2KNMMpbrOnJBn1NevbuFbMRoqJE77u9e4Hq1eWOirJtyhTRZtbYWBQgfPqp3BERGZzwcPE/iI8PcP168nZHR3EFul8/MUBLeYNJTzboW9KjUokFQydPFo+bNhVt2Ll+Vj6nXo3999+BggVFv4EKFeSOisggSRJw8aJIfrZuTXmpq3FjMfrTtStgbS1biAaBhcwGLipKdCNVJzzDhwOHDzPh0QsKhejd06CB+Avr6SmaF/J/F6I8p1AAbm7A0qWi3mf7dtFlQqkU3aAHDACKFxcjP/7+nIOgCzjS8x99GekJDhb1O1evikVCly0TPe5Izzx/Lqay378vHjdoILo4N24sb1xEhNBQYONGUT95507ydldXkQB5eYlyA9IOjvQYqL//Fq1crl4Vqw77+zPh0VtFi4op7BMmiDVD/vkHaNJETNELCpI7OiKDVrKkWEXm1i3RTP2rr8QlruBgUZbn6gq0aCHqgmJi5I7WsHCk5z/5eaRHvWDomDFiRoGbm5jhXKqU3JFRnnjyBPjpJ2DNGtGMCQB69hQFz6ymJNIJMTFizS8fH/EPqpq1tVgBvn9/MXjLZYCyjoXM2ZBfk564OGDoUFHmAYiZWqtWccFQg3Tvnijk+v138djYWLTenjRJFBYQkU54+DD58ldwcPL28uXF5a8+fcRoEWUOk55syI9Jz9OnYsHQM2dE4dwvv4jRHv6nYOAuXRINDP/8Uzy2sBDd1b79VnR4JiKdoFIBJ06I5GfHjuRLXUol0LKlGP1p3170AqL0MenJhvyW9Jw7JxpiPXkiZi5v3y5+SYg0jh8XhQUBAeJxwYKiBmjECK7fRaRj3r4Vic/69WLml1qhQuJqddeuQMOGojE7pcSkJxvyU9KzcSPw9dfJC4bu28fSDUqHJIkp7T/8AFy7JrYVLy6qKQcMEFP8iEin3Lsnkp8NG4B//03eXqCA6EfaqpW4lS4tW4g6hUlPNuSHpCcxUVyh+PVX8bh9e7Fiuo6GS7okKUl0T5s8WRQUACJT/ukn0dRJyYmcRLomKUkUPW/ZAvj6ik7Q7ytXTrTqatVKNKAtUECWMGXHpCcbdD3pefVKVPgfPSoeT5oETJ3K9yrKorg4YPVqkew8eya21agBzJol/nqyIIxIJ6lUwJUrIvnx9RVT4dWTNQFx2atJk+QkqHJlw/l1ZtKTDbqc9Fy/LkZ1HjwQpRgbNojru0TZFhUFLFwoqt8jI8W2Jk1E8tOggayhEdHHRUaKUaC//hJzFh49Svl8yZLJl8FatBAlffqKSU826GrSs2ePmL4YFQW4uIgFQ6tVkzsq0hsvXohOzkuWiFEgQGTYM2cCVarIGxsRZYokic7Pvr4iCTp2DHj3Lvl5IyPA3T05CapdW7+uEjDpyQZdS3pUKmDGDFFvCgDNmokFQ+3s5I2L9NTjx6KZ4bp14odPoRDZ9rRpItsmonwjNlbMAFNfCrt5M+XzdnZitq+np/hYrJg8cWoLk55s0KWkJypKrM2ya5d4PGIEMH8+J9pQHrh1SxSM7dwpHpuYAIMHi9lfDg7yxkZE2RISIkaAfH1FXaj6irZazZpiBMjTU1zdzm/vNUx6skFXkp4HD8SCodeuicK05cvFzGKiPHX+PPD998mV8wUKAN7ewNixgK2tvLERUbYlJABnzyaPAl28mPJ5a2ugefPkJCg/DPQy6ckGXUh6/PzE7OFXr8Rw465dYi0WItn4+YkGh+fPi8dFiohkaOhQtokl0gPPngGHD4sE6PBh4PnzlM9XqJA8I8zDQzeXOGLSkw1yJj2SBCxeLP6RTkoSK6Xv3s21V0hHSJL4gfzhB3H5CxCr2U6dKq7DGhvLGh4RaYdKJVaxUY8CBQSI9yQ1c3OR+KhHgSpU0I1p8Ux6skGupCcuDhgyRKy8CwB9+wIrV/KfaNJBiYmiHfjUqaLwGRArJM6cKRaB04W/fkSkNW/eiGnx6iRI/Wuv5uSUPCPs00/lu/LNpCcb5Eh6njwR7xVnz4rpg/Pni3Uh+d5BOu3dO1FsNnMm8PKl2ObmJqa+N28ub2xElCskScwCUxdEHz+e3OUCENPiGzRIToJq1Mi7afFMerIhr5Oes2fFgqFPn4oF5bZvBz77LNdPS6Q9kZEiU58/H4iOFtuaNxcNDuvUkTc2IspVMTEi8VH3Brp9O+Xz9vbiEph6WnzRorkXC5OebMjLpGfDBrFgaHw8UKmSaDjIBUMp33r2DPj5ZzH6Ex8vtnXpIhpNVaggb2xElCeCg5NHgfz8ROsVNYVCNERU1wI1bKjdKxpMerIhL5KexERg/HjR/R8QU9M3bRJTBInyvYcPRb3Pxo1iLFypBPr3Fx02HR3ljo6I8kh8vCiCVtcCBQUlP/fJJ6lHhXKKSU825HbS8/KlWDDUz088njxZvBfoUytwIgCiydSPP4ohTAAwMwOGDRNT39lSnMjghIUlT4svV040etcmJj3ZkJtJz7VrYlTnwQPR423jRlHATKTXzpwBJkwQF/4BMaQ5fjwwZgxgZSVvbESkN7Ly/s1xhlz2119AvXoi4XF1FUN+THjIINSrJ1Y+9PUVfe7fvhVDnKVLA7/9lnLqBxFRHmDSk8tcXUXvtk8/FU1tq1aVOyKiPKRQiMrFCxeAbdtExf7z56I3Q/nyYtjz/e5nRES5iElPLvvkE+DUKTHiU6SI3NEQyUSpFEVtN26I7pslSgCPHomOztWrAzt2AK9fyx0lEek51vT8RxfW3iIyGDExwJIloqHh+8lOxYpiwbl69cTHSpVY7U9EGWIhczYw6SGSwZs3wLx5ojvnvXupn7exAdzdRQJUv764X6hQnodJRLqLSU82MOkhktnz52LGV0CAuJ07J0aEPlShQnISxNEgIoPHpCcbmPQQ6ZjERNHvQZ0EBQSkPxpUt25yElSvHkeDiAwIk55sYNJDlA+oR4PUI0LnziWv+/W+90eD6tUTo0FGRnkfLxHlOiY92cCkhygfen80SJ0I3b2bej9r69S1QYUL5328RKR1THqygUkPkZ548SJ1bVBao0Hly6euDeJoEFG+w6QnG5j0EOmppKTUtUEZjQapp8vXq8fRIKJ8gElPNjDpITIgL14AZ8+mHA2Kikq93/ujQfXqAZUrczSISMcw6ckGJj1EBkw9GvT+ZbE7d1LvZ22dcqaYuztbrRPJjElPNjDpIaIUXr5MToLOnBEjQ2mNBn3ySXIS5OYGlCwJ2NmJRfeIKNcx6ckGJj1ElKGkJOD69ZS1QWmNBgFioVU7O8DeHnBwELf377//2N4eMDfP28+FSI8w6ckGJj1ElGUvX6asDbpyRdQLZfXPqo1N2glRWo+trERSRUQAmPRkC5MeItKKxESRDIWHi9uzZ8n3P3z87BmQkJC141tYpD+C9GGyVKgQl+ggvZeV929edCYi0iZj4+Sk42MkSSy6mpnkKDxc9BuKjQUePRK3zMRStOjHR4/s7cV+JiY5/vSJdJlOJz1Lly7FL7/8grCwMFSvXh2LFy9G3bp1091/x44dmDRpEh4+fIhy5cphzpw5aN26dR5GTESUBQqFGI0pVEgsnfEx0dGZS47Cw4HXr8Wo09On4pYZRYqIJKhoUcDSUowqWViImiP1/Yy2fWxfExNemiNZ6WzSs337dnh7e2PFihVwd3fHwoUL4enpidu3b8Pe3j7V/v/88w969uyJWbNmoW3btti6dSs6duyIwMBAVKlSRYbPgIhIywoUAFxdxe1j4uPFWmWZGUV6/lwUar98KW65RanMeiKVneTq/cfGxuK8TLYIOlzT4+7ujjp16mDJkiUAAJVKBUdHR4wYMQITJkxItf8XX3yB6OhoHDhwQLOtXr16qFGjBlasWPHR87Gmh4gMlkolkh11MvTiBRATIy6lxcYC794l389oW3rbdYGRkbgZG6e+n9a2rN7P7dcpFOKmTuDkeKyNY5mbZ+7Sbxbk+5qe+Ph4XLx4ERMnTtRsUyqVaNGiBQICAtJ8TUBAALy9vVNs8/T0xJ49e9LcPy4uDnFxcZrHkZGROQ+ciCg/UirFJa2iRUXXaW2SJDHqlJOkKTv7fvj/fFKSuMXHa/fzo6ypXx/45x/ZTq+TSc+LFy+QlJQEhw+yQQcHB9y6dSvN14SFhaW5f1hYWJr7z5o1C9OmTdNOwERElDaFAjAzE7eCBfPmnOpE6907UdeUmJic9GT3vjaOkd3jJSaKz0l9U6m091ibx8rMYzOzvPkZSIdOJj15YeLEiSlGhiIjI+Ho6ChjREREpBXvJ1pE79HJpMfOzg5GRkYIDw9PsT08PBzFihVL8zXFihXL0v5mZmYw4y8EERGRwdDJrlWmpqaoXbs2/Pz8NNtUKhX8/PxQv379NF9Tv379FPsDwJEjR9Ldn4iIiAyLTo70AIC3tze8vLzg5uaGunXrYuHChYiOjkb//v0BAH379kXJkiUxa9YsAMCoUaPg4eGB+fPno02bNti2bRsuXLiAVatWyflpEBERkY7Q2aTniy++wPPnzzF58mSEhYWhRo0a8PX11RQrh4SEQPlee/UGDRpg69at+PHHH/H999+jXLly2LNnD3v0EBEREQAd7tOT19inh4iIKP/Jyvu3Ttb0EBEREWkbkx4iIiIyCEx6iIiIyCAw6SEiIiKDwKSHiIiIDAKTHiIiIjIITHqIiIjIIDDpISIiIoPApIeIiIgMgs4uQ5HX1I2pIyMjZY6EiIiIMkv9vp2ZBSaY9Pzn7du3AABHR0eZIyEiIqKsevv2LWxtbTPch2tv/UelUuHJkyewtraGQqHQ6rEjIyPh6OiIx48fc10vHcDvh27h90O38Puhe/g9yZgkSXj79i1KlCiRYiHytHCk5z9KpRKlSpXK1XPY2NjwB1aH8PuhW/j90C38fugefk/S97ERHjUWMhMREZFBYNJDREREBoFJTx4wMzPDlClTYGZmJncoBH4/dA2/H7qF3w/dw++J9rCQmYiIiAwCR3qIiIjIIDDpISIiIoPApIeIiIgMApMeIiIiMghMenLZ0qVL4eLiAnNzc7i7u+PcuXNyh2SwZs2ahTp16sDa2hr29vbo2LEjbt++LXdY9J/Zs2dDoVBg9OjRcodisEJDQ/Hll1+iSJEisLCwQNWqVXHhwgW5wzJISUlJmDRpElxdXWFhYYEyZcrgp59+ytT6UpQ+Jj25aPv27fD29saUKVMQGBiI6tWrw9PTE8+ePZM7NIN0/PhxDBs2DGfOnMGRI0eQkJCAli1bIjo6Wu7QDN758+excuVKVKtWTe5QDNbr16/RsGFDmJiY4M8//8SNGzcwf/58FCpUSO7QDNKcOXOwfPlyLFmyBDdv3sScOXMwd+5cLF68WO7Q8jVOWc9F7u7uqFOnDpYsWQJArO/l6OiIESNGYMKECTJHR8+fP4e9vT2OHz+OJk2ayB2OwYqKikKtWrWwbNkyzJgxAzVq1MDChQvlDsvgTJgwAadPn8bJkyflDoUAtG3bFg4ODli7dq1mW5cuXWBhYYHNmzfLGFn+xpGeXBIfH4+LFy+iRYsWmm1KpRItWrRAQECAjJGRWkREBACgcOHCMkdi2IYNG4Y2bdqk+F2hvLdv3z64ubmhW7dusLe3R82aNbF69Wq5wzJYDRo0gJ+fH+7cuQMAuHz5Mk6dOoXPP/9c5sjyNy44mktevHiBpKQkODg4pNju4OCAW7duyRQVqalUKowePRoNGzZElSpV5A7HYG3btg2BgYE4f/683KEYvAcPHmD58uXw9vbG999/j/Pnz2PkyJEwNTWFl5eX3OEZnAkTJiAyMhIVKlSAkZERkpKSMHPmTPTu3Vvu0PI1Jj1kkIYNG4Zr167h1KlTcodisB4/foxRo0bhyJEjMDc3lzscg6dSqeDm5oaff/4ZAFCzZk1cu3YNK1asYNIjgz/++ANbtmzB1q1bUblyZQQFBWH06NEoUaIEvx85wKQnl9jZ2cHIyAjh4eEptoeHh6NYsWIyRUUAMHz4cBw4cAAnTpxAqVKl5A7HYF28eBHPnj1DrVq1NNuSkpJw4sQJLFmyBHFxcTAyMpIxQsNSvHhxVKpUKcW2ihUr4n//+59MERm28ePHY8KECejRowcAoGrVqnj06BFmzZrFpCcHWNOTS0xNTVG7dm34+flptqlUKvj5+aF+/foyRma4JEnC8OHDsXv3bvz9999wdXWVOySD1rx5c1y9ehVBQUGam5ubG3r37o2goCAmPHmsYcOGqVo43LlzB87OzjJFZNhiYmKgVKZ8izYyMoJKpZIpIv3AkZ5c5O3tDS8vL7i5uaFu3bpYuHAhoqOj0b9/f7lDM0jDhg3D1q1bsXfvXlhbWyMsLAwAYGtrCwsLC5mjMzzW1tap6qkKFCiAIkWKsM5KBmPGjEGDBg3w888/o3v37jh37hxWrVqFVatWyR2aQWrXrh1mzpwJJycnVK5cGZcuXcKCBQswYMAAuUPL1zhlPZctWbIEv/zyC8LCwlCjRg389ttvcHd3lzssg6RQKNLc7uPjg379+uVtMJSmpk2bcsq6jA4cOICJEyfi7t27cHV1hbe3NwYNGiR3WAbp7du3mDRpEnbv3o1nz56hRIkS6NmzJyZPngxTU1O5w8u3mPQQERGRQWBNDxERERkEJj1ERERkEJj0EBERkUFg0kNEREQGgUkPERERGQQmPURERGQQmPQQERGRQWDSQ0RERAaBSQ+RzFxcXKBQKKBQKLBz585092vRogUUCgXWr1+fd8FlQ9OmTaFQKODv7y93KLlu//79aNy4MWxsbDTfQ335vKdOnQqFQoGpU6fKHQqR1nDtLSId8sMPP6Bjx44wNuavpq4LCgpCly5doFKp8Omnn6J48eJQKBQoVqyY3KERUTr4l5VIR1haWuLOnTtYs2YNBg8eLHc49BF79uxBQkICvv/+e8ycOVPucIgoE3h5i0hHjBo1CgAwffp0xMTEyBwNfUxISAgAoFy5cjJHQkSZxaSHSEe0bt0aHh4eePr0KX799ddMv65fv34Z1vqsX78eCoUi1Ury72+PiIiAt7c3XFxcYG5ujnLlymHOnDlQqVQAgNDQUHzzzTdwdHSEmZkZypcvj8WLF380tuPHj6Nly5YoXLgwLC0tUbduXWzatCnD1/j5+aFz584oXrw4TE1NYW9vj06dOiEgICDN/dW1NADg4+OD+vXrw9bWFgqFAg8fPvxojACQmJiIFStWoEGDBrC1tdV8DUaOHInQ0NAU+6prXXx8fAAA/fv318TQtGnTTJ0PAK5du4YuXbrAzs4OlpaWqFq1KhYuXAiVSqWp80or/levXuH7779H5cqVYWlpCWtra9SuXRtz585FbGxsmufatWsXvvrqK1SpUgWFChWCubk5XF1dMWDAANy+fTvTMavt2LEDLVq0QJEiRWBiYoIiRYqgUqVKGDRoEK5cuZLl4xHlFSY9RDpkzpw5AIC5c+fi5cuXeXLON2/eoH79+tiyZQvc3Nzg4eGB0NBQTJgwAaNGjcL9+/fh5uaGP//8Ew0aNEDDhg1x//59jBw5UhNvWnbv3o1PP/0UoaGh8PT0RJ06dXDx4kX07dsXY8eOTfM148aNQ4sWLbB37144OTmhY8eOKF26NPbu3YvGjRtrEo20jBgxAl999RWMjY3Rpk0buLu7a5KhjMTFxeHzzz/HkCFDcOnSJTRs2BAdO3ZEXFwcFi9ejBo1aiAwMFCzf40aNeDl5YUyZcoAABo2bAgvLy94eXmhVatWHz0fIJLBunXrYteuXShYsCA6dOiA4sWL47vvvkOvXr3Sfd2DBw9Qq1YtzJo1C8+fP0fr1q3x6aef4u7du/juu+/QqFEjvH79OtXrunfvjt9//x0WFhb49NNP4enpCaVSCR8fH9SuXRv//PNPpuIGxEhk9+7dcfz4cVSpUgXdunVDvXr1YGRkhLVr1+Lvv//O9LGI8pxERLJydnaWAEgnT56UJEmSOnfuLAGQxowZk2K/5s2bSwAkHx+fFNu9vLzS3K7m4+MjAZC8vLzS3A5AateunRQdHa157uLFi5KxsbGkVCqlSpUqSYMHD5YSEhI0z+/Zs0cCINnY2KR4nSRJkoeHh+a4P//8c4rn/P39JQsLCwmA5Ovrm+K5VatWSQCksmXLSpcvX07x3PHjxyVra2vJ1NRUunPnTorn1OeysbGRAgIC0vwaZOS7776TAEhlypSRgoODNdvj4+OlgQMHSgAkV1dXKS4uLsXrPvZ1T09MTIxUsmRJCYA0duxYKSkpSfPc9evXJQcHB83n9H48kiRJ7u7uEgCpffv2UlRUlGb7s2fPpFq1akkApF69eqU657Zt21LsL0mSpFKppKVLl0oApMqVK0sqlSrF81OmTJEASFOmTNFse/funWRhYSFZWVlJt27dSnWehw8fSjdv3szKl4MoTzHpIZLZh0nPrVu3JGNjY8nMzEx6+PChZr/cSnqsrKyk8PDwVK9r3769BEBycnKSYmNjUz1ftWpVCYB0/PjxFNvVSU/NmjXTjGfs2LESAOmzzz7TbEtKSpJKlCghAZAuXLiQ5uvmzp2rSRTep04Qpk+fnubrMhIbGytZWVlJAKR9+/alej46OlqThGzZsiXFc9lNejZu3CgBkJydnaX4+PhUzy9ZsiTNpOfkyZMSAMnS0lIKCwtL9boLFy5IACSlUik9fvw40/HUr19fAiBdv349xfa0kp5nz55JAKRq1apl+vhEuoSXt4h0TPny5TFgwADExcVh0qRJuX6+2rVrw97ePtV2dYFus2bNYG5unu7zT548SfO4ffv2TXO7l5cXAODUqVNISkoCAFy6dAlPnjxBmTJlULt27TRfp66XSe9STNeuXdPcnpELFy4gKioKhQsXRrt27VI9b2lpiR49egAAjh07luXjp+X48eMAgG7dusHExCTV8717907zder+P61atYKDg0Oq52vXro3q1atDpVJpzvG+e/fuYcmSJRg9ejQGDhyIfv36oV+/fggPDweATNX2FC1aFC4uLrhy5QrGjh2LGzdufPQ1RLqEU9aJdNDUqVOxefNmbNmyBePGjUO1atVy7VxOTk5pbreyssrweWtrawDAu3fv0nze1dU1w+2xsbF4+fIl7O3t8eDBAwDA/fv3P1qH8/z58zS3u7i4ZPi6tKiLlNOLFYCmdufDgubs+vfffwGkH2/BggVha2uLiIiIFNszG+vly5dTxJqUlIThw4dj5cqVkCQp3ddGRkZmKv6NGzeia9euWLBgARYsWIDChQvD3d0dn332Gfr06QM7O7tMHYdIDkx6iHRQ8eLFMWrUKMyaNQsTJ07EwYMHs30s9Qys9CiVGQ/4fuz5nFC/CatjLFasGDw9PTN8TXpvqhYWFtoNLpdllNxlpgA7sxYtWoQVK1agWLFiWLBgARo0aAAHBwfN6F2vXr3w+++/Z5gQva9x48Z4+PAhDh48iOPHj+Off/7BX3/9hT///BNTpkzB7t270bx5c63FT6RNTHqIdNR3332HVatW4dChQzhx4kS6+5mamgIA3r59m+bzjx49ypX4PiY4ODjN7epp2Obm5ihSpAgAwNHREQBQpEiRPF1mo2TJkgDSjxWAZhRKva+2zpnedPqIiAi8efMm3dep40lLWrH+8ccfAICVK1eiffv2qV5z9+7dTMX9PgsLC3Tt2lVzSfH58+f48ccfsWrVKgwYMEC2nzmij2FND5GOsrW1xffffw8A+Pbbb9PdT/0Gd/PmzVTPSZKEP//8M3cC/IjNmzenuX3jxo0AgEaNGmmW26hTpw7s7Oxw48YNXL9+Pc9idHNzg5WVFV69eoV9+/alej42Nhbbtm0DIGqbtKFJkyYARK+bxMTEVM9v3bo1zdepa5p8fX01dTjvu3TpEoKCgqBUKjXnAERfHwBwdnZO9Zrr168jKCgoq59CKkWLFsXcuXMBiKaNaU2bJ9IFTHqIdNiwYcPg5OSEs2fPptucr0WLFgCATZs2pSgsTUhIwHfffYfz58/nSawfunjxouaNUO3UqVNYunQpAGDMmDGa7SYmJpgyZQokSUKnTp1w6tSpVMdLSkrC33//jTNnzmgtRnNzcwwbNgwAMHbs2BQjFAkJCRg1ahTCwsLg6uqarULptHTr1g3FixfHw4cP8cMPP6S4/Hjr1i1Mnz49zdc1atQI7u7uiI2NxTfffJOia/eLFy/wzTffAAB69OihGTkDgIoVKwIAli5dmuJcT58+Rd++fdNMvNLz6NEjrFmzJs36n/379wMAChUqBBsbm0wfkygv8fIWkQ4zMzPD9OnT0a9fv3SXpmjYsCE6dOiAvXv3ws3NDY0aNYKFhQUCAwMRGRmJUaNGYdGiRXkcOTBy5EhMnDgRGzduRLVq1fDkyROcPHkSKpUKo0aNQuvWrVPsP3z4cISEhOCXX35B48aNUblyZZQtWxYWFhYICwtDUFAQ3rx5g+XLl6NevXpai3PatGm4cOEC/Pz8ULFiRTRr1gzW1tYICAhASEgIihQpgh07dmguI+aUpaUlNm/ejDZt2mDu3LnYtWsX3Nzc8OrVK/j7+6NDhw44e/YsQkJCUp1z69at+PTTT7F37164urqiSZMmSEhIwLFjxxAZGYlatWphyZIlKV7z/fffw9fXF6tXr8axY8dQq1YtREZG4vjx4yhdujQ6deqE3bt3Zyr2169fY9CgQRg6dChq1KihKaq+e/cuLl26BIVCgV9++QVGRkZa+VoRaRtHeoh0XJ8+fVC1atUM99m+fTt+/PFHFC9eHP7+/jhz5gwaN26MwMBA1KhRI28C/UCnTp1w5MgRFCtWDIcOHcK5c+dQq1YtrF+/HgsXLkzzNXPnzsXp06fRu3dvREVFwdfXFwcPHsSTJ0/QtGlTrFmzBl988YVW4zQzM4Ovry+WLVuG6tWr4+TJk9i9ezdMTEwwYsQIXL58Od1p9Nn16aef4uzZs+jUqRNevXqFPXv24N9//8XMmTOxefNmhIWFQalUonDhwileV7p0aQQGBmLixIkoUqQIDhw4gCNHjqBMmTKYPXs2Tp06hUKFCqV4jbu7Oy5cuID27dsjOjoa+/btw/379zFixAgEBARkaVSmTJkyWLhwIdq2bYs3b97g0KFDOHjwIKKjo9G3b1+cP38eAwcO1MrXiCg3KKTMluwTEVGuO3HiBDw8PFC1alWuY0WkZRzpISLKY8+fP09zxti1a9cwaNAgAGIhUyLSLo70EBHlMX9/fzRr1gyVKlVC6dKlYWFhgeDgYAQGBkKlUuGzzz7DoUOHNLPbiEg7mPQQEeWxJ0+e4Oeff8bx48cRGhqKt2/fwtraGpUrV0avXr0waNAgJjxEuYBJDxERERkE1vQQERGRQWDSQ0RERAaBSQ8REREZBCY9REREZBCY9BAREZFBYNJDREREBoFJDxERERkEJj1ERERkEP4PPFnvg3CZ5CAAAAAASUVORK5CYII=\n"
},
"metadata": {}
}
],
"source": [
"pred_liv=make_mixture(pmf_table,liv['probs'])\n",
"pred_man=make_mixture(pmf_table,man['probs'])\n",
"plt.plot(range(10), pred_liv, color=\"blue\")\n",
"plt.plot(range(10),pred_man, color=\"red\")\n",
"plt.legend(['Liverpool', 'Manchester United'], fontsize = 14, loc = 'best')\n",
"plt.xlabel('Number of goals', size = 16)\n",
"plt.ylabel('Probability', size = 16);"
]
},
{
"cell_type": "markdown",
"id": "ae653a76-a33e-4ce2-b018-04e84f1e200a",
"metadata": {
"id": "ae653a76-a33e-4ce2-b018-04e84f1e200a"
},
"source": [
"---"
]
}
],
"metadata": {
"kernelspec": {
"display_name": "Python 3",
"name": "python3"
},
"language_info": {
"codemirror_mode": {
"name": "ipython",
"version": 3
},
"file_extension": ".py",
"mimetype": "text/x-python",
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
"version": "3.9.13"
},
"colab": {
"provenance": [],
"gpuType": "T4"
},
"accelerator": "GPU"
},
"nbformat": 4,
"nbformat_minor": 5
}