{
  "cells": [
    {
      "cell_type": "markdown",
      "id": "963b7001-be41-4c01-9242-975ceaf152ca",
      "metadata": {
        "id": "963b7001-be41-4c01-9242-975ceaf152ca"
      },
      "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": "3a96b100-064e-4a6a-af6d-12fd2dd625eb",
      "metadata": {
        "id": "3a96b100-064e-4a6a-af6d-12fd2dd625eb"
      },
      "source": [
        "## The Problem: Weights of Elephants 35 Points (5 Points Bonus)\n",
        "\n",
        "Suppose we choose two elephants from a population; let's call them elephant A and elephant B. If we see that A weighs more than B, what is the weight of A?\n",
        "\n",
        "### Approaching the Problem\n",
        "\n",
        "1: Establish a prior for A's weight: we can use background information about the weight of elephants.\n",
        "\n",
        "2: Construct a joint prior distribution of weight for A and B.\n",
        "\n",
        "3: Update the prior with the information that A is heavier.\n",
        "\n",
        "4: From the joint posterior distribution extract the posterior distribution of weight for A.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f86583a7-da47-4f42-b6f3-15323f65f741",
      "metadata": {
        "id": "f86583a7-da47-4f42-b6f3-15323f65f741"
      },
      "source": [
        "The Prior\n",
        "\n",
        "The average weight of an adult African elephant is about 6000 kg, and the standard deviation is roughly 500 kg, and is approximately normal.\n",
        "\n",
        "We can use that as the prior distribution for the weights of both elephant A and B."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "028e0afb-0487-4564-ab30-0996173f00cc",
      "metadata": {
        "id": "028e0afb-0487-4564-ab30-0996173f00cc"
      },
      "source": [
        "Start by importing the necessary libraries. We will need `pandas` for data manipulation, `numpy` for numerical operations, and `scipy.matplotlib` for visualization."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "id": "2943cd49-9092-4e06-b7b4-96224d32fb39",
      "metadata": {
        "id": "2943cd49-9092-4e06-b7b4-96224d32fb39"
      },
      "outputs": [],
      "source": [
        "from scipy.stats import norm\n",
        "\n",
        "# Add any additional libraries you think you'll need below this line.\n",
        "\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "\n",
        "# Additional libraries\n",
        "import seaborn as sns  # For better visualization"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "b9d65e0d-6468-46ad-877a-8378297a34e8",
      "metadata": {
        "id": "b9d65e0d-6468-46ad-877a-8378297a34e8"
      },
      "source": [
        "# Prior Plotting - 5 Points"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "id": "4adcd9e4-01da-47db-8072-9dc675ff65fd",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 478
        },
        "id": "4adcd9e4-01da-47db-8072-9dc675ff65fd",
        "outputId": "ff2c2196-c56a-4758-943c-f781c6a19807"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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exqIKAOLi4qDVapGVlQUA6NmzJ7RaLT799FNUVFSgqKgI//nPfxAXF6dYVJWWlkKv15vciMg23b4NrFoFzJ0L/PCDclEFALduSQXYwoXAihUAP/5E9s+qCqsbN26goqIC/v7+Jsf9/f2h0+nM3ken0ym2r/xaUxs/Pz+TuKOjI3x8fIxtwsLCsGXLFrz22mtwcXGBt7c3Ll++jLVr1yqe06JFi+Dl5WW8BQcHK7YnIut0+DCwYAGwc2fdh/iEADIzpQLrwIEGSY+IrIRVFVbWTKfTYfLkyRg/fjyys7OxY8cOODs745lnnoHSaOqcOXNQVFRkvF26dEnFrInoQQkBbNgA/O1vD97jVFIC/OMfwNq1nH9FZK8cGzuBqnx9feHg4ID8/HyT4/n5+QiQmaAQEBCg2L7ya35+PgIDA03aREVFGdvcPzm+vLwcBQUFxvsvW7YMXl5eWLx4sbHN559/juDgYGRlZaFv375m83NxcYGLi0tNp05EVqiiAvj3v6W5VJaUkSHN0/rtb4FaTs8kIhthVT1Wzs7O6NmzJzIyMozHDAYDMjIyEBMTY/Y+MTExJu0BID093dg+LCwMAQEBJm30ej2ysrKMbWJiYlBYWIicnBxjm61bt8JgMCA6OhoAcPv2beOk9UoODg7GHInIvlRUAJ98YvmiqtKhQ1IvWHl5wzw+ETUOqyqsACAlJQXLly/HypUrkZubi5deegklJSWYOHEiAGDcuHGYM2eOsf20adOQlpaGJUuW4OTJk1i4cCH279+P5ORkAIBGo8H06dPx9ttvY8OGDTh69CjGjRuHoKAgJCQkAAA6deqE4cOHY/Lkydi3bx92796N5ORkjBkzBkFBQQCAkSNHIjs7G2+++SbOnDmDAwcOYOLEiQgJCUGPHj3UfZGIqEEJAXz6ae3nQ4WHAyNHAmPHAk88AUREABpNzfc7cUIq3vi3GZH9sKqhQEBaPuH69euYP38+dDodoqKikJaWZpx8fvHiRZOeo379+mH16tWYO3cuXnvtNYSHh2P9+vXo2rWrsc2sWbNQUlKCKVOmoLCwELGxsUhLS4Orq6uxzapVq5CcnIxhw4ZBq9Vi9OjRWLp0qTE+dOhQrF69GosXL8bixYvRrFkzxMTEIC0tDW5ubiq8MkSklo0bgezsmtt16QI8+yxQZZaB0bVrwDffAAcPKj/GwYPSnKsxY+qXKxFZF6tbx8recR0rIuuWnS31IilxcJB6p2JjlXumhAD27QP+8x+grEz5MceNA/r3r3u+RKQOm1zHioioMf38M/DZZ8ptmjUDUlKAAQNqHu7TaIDoaGDmTMDDQ7nt6tXAhQt1y5eIrA8LKyIiSD1Kn3wC3Lsn38bNDZg2DWjfvm6PHRoqFWPu7vJtysul5y8trdtjE5F1YWFFRATgv/+V9v2T4+gIJCdLRVJ9BAVJRZnS6ivXrgHr1tXv8YnIOrCwIqIm76efpK1nlLzwQt17qu4XEgL87wJnWbt2AcePP9jzEFHjYWFFRE1aebk0uVzpMp4hQwCZNYDrrEcPYMQI5TarVysPSRKR9WJhRURN2vffA1evysfbtAFGj7bscz7xBPDQQ/LxGzeA776z7HMSkTpYWBFRk3XjBrB5s3zc0RGYPNny285otcCLLwJVltKrZssW5YKPiKwTCysiarK+/lp5S5nHHwdktil9YL6+wNNPy8cNBmDNGuUhSiKyPiysiKhJOntWecua1q2BRx9t2BwGDgTCwuTjJ09yIjuRrWFhRURNjhDKyxpoNNJVgP/bZ73BaDTA889LQ4Nyvv6aewkS2RIWVkTU5OzfD5w/Lx+PiVHuSbKkNm2AoUPl41evAnv2qJMLET04FlZE1KQYDNImy3JcXIBRo9TLBwBGjpS2ypGzcWPNew0SkXVgYUVETcq+fUB+vnw8Ph7w9lYtHQBSUTVypHy8sBD48UfV0iGiB8DCioiaDINBeX0ob2/gkUdUS8fE4MHSlYJy0tKUr2AkIuvAwoqImoy9e6X9+OSMGAE4O6uXT1WOjkBCgnycvVZEtoGFFRE1CUJIvT5yfHyA/v3Vy8ecnj2V181irxWR9WNhRURNwuHDynOrRoyQeo0ak1arPNfql1+kOWJEZL1YWBFRk/D99/Kxli2lJRasQa9egL+/fDw9nauxE1kzFlZEZPfOnQN++kk+Hh/f+L1VlWrqtbp6FThxQr18iKhuWFgRkd1T6q1q3hzo10+9XGqjd2+pF01Oerp6uRBR3bCwIiK7lp8PHDkiHx8yBHByUi+f2tBqgWHD5OO5ucClS+rlQ0S1x8KKiOza1q3yc5KcnKT1o6xR//6Am5t8/Icf1MuFiGqPhRUR2a27d4HMTPl4//7SUKA1cnUFBgyQj2dnA3q9evkQUe2wsCIiu7V3L1Baaj6m0QBxcermU1dDh0rDguZUVAC7d6ubDxHVjIUVEdklIYAdO+TjkZFAq1bq5VMfLVpIE9nl7NolbdNDRNaDhRUR2aUzZ6SlCeRY69yq+ynlefMmcPy4aqkQUS2wsCIiu7R9u3zMzw/o3Fm1VB5IWBgQHCwfV+qVIyL1sbAiIrtTVAQcPCgfHzRImmNlCzQaKV85x45JPVdEZB1YWBGR3dm7V37ukZOT9S0IWpM+faSrBM0RQpprRUTWgYUVEdkVIZSvluvTB2jWTL18LMHFRXkvwz17OImdyFqwsCIiu/LTT9Jq63IGDlQvF0tSyruoiPsHElkLqy2sli1bhtDQULi6uiI6Ohr79u1TbL9u3TpERETA1dUVkZGR2Lx5s0lcCIH58+cjMDAQbm5uiIuLw5kzZ0zaFBQUICkpCZ6envD29sakSZNw69YtY3zhwoXQaDTVbu7u7pY7cSJ6IEq9VUFBQEiIerlYUlAQ0L69fHzPHvVyISJ5VllYrVmzBikpKViwYAEOHDiA7t27Iz4+HteuXTPbfs+ePRg7diwmTZqEgwcPIiEhAQkJCTh27JixzeLFi7F06VKkpqYiKysL7u7uiI+Px927d41tkpKScPz4caSnp2PTpk3YuXMnpkyZYozPnDkTP//8s8mtc+fOePbZZxvuxSCiWistBfbvl4/37287k9bNUZobdvgwUFKiXi5EZJ5GCLldtBpPdHQ0evfujY8//hgAYDAYEBwcjKlTp2L27NnV2icmJqKkpASbNm0yHuvbty+ioqKQmpoKIQSCgoIwY8YMzJw5EwBQVFQEf39/rFixAmPGjEFubi46d+6M7Oxs9OrVCwCQlpaGESNG4PLlywgKCqr2vIcPH0ZUVBR27tyJAUp7T1Sh1+vh5eWFoqIieHp61vm1ISJ5e/YAK1eaj2m1wOLFgIeHujlZ0t27wCuvAPfumY+PHWs763MR2Zra/v62uh6re/fuIScnB3FV9prQarWIi4tDpsymX5mZmSbtASA+Pt7YPi8vDzqdzqSNl5cXoqOjjW0yMzPh7e1tLKoAIC4uDlqtFllZWWaf95NPPkGHDh0Ui6rS0lLo9XqTGxE1DKXhsO7dbbuoAqQrAx9+WD7O4UCixmd1hdWNGzdQUVEBf39/k+P+/v7Q6XRm76PT6RTbV36tqY2fn59J3NHRET4+Pmaf9+7du1i1ahUmTZqkeD6LFi2Cl5eX8RastNIfEdXbtWvSautybG2JBTn9+8vHLlwArlxRLxciqs7qCitb8d///hfFxcUYP368Yrs5c+agqKjIeLt06ZJKGRI1LTIdywAAT0+ga1f1cmlI4eGAr698nL1WRI3L6gorX19fODg4IP++66Xz8/MREBBg9j4BAQGK7Su/1tTm/snx5eXlKCgoMPu8n3zyCR5//PFqvWD3c3Fxgaenp8mNiCxLCOXCKiZGmmNlDzQa5TWtsrK4phVRY7K6HzXOzs7o2bMnMjIyjMcMBgMyMjIQI/PTJCYmxqQ9AKSnpxvbh4WFISAgwKSNXq9HVlaWsU1MTAwKCwuRk5NjbLN161YYDAZER0ebPHZeXh62bdtW4zAgEanjwgXg+nX5uFIhYouUzqe4GDh1Sr1ciMiU1RVWAJCSkoLly5dj5cqVyM3NxUsvvYSSkhJMnDgRADBu3DjMmTPH2H7atGlIS0vDkiVLcPLkSSxcuBD79+9HcnIyAECj0WD69Ol4++23sWHDBhw9ehTjxo1DUFAQEhISAACdOnXC8OHDMXnyZOzbtw+7d+9GcnIyxowZU+2KwH//+98IDAzEY489ps4LQkSKlHqrgoOBwED1clFDy5ZAx47y8RqW/SOiBuTY2AmYk5iYiOvXr2P+/PnQ6XSIiopCWlqacdjt4sWL0Fbp1+/Xrx9Wr16NuXPn4rXXXkN4eDjWr1+PrlUmVcyaNQslJSWYMmUKCgsLERsbi7S0NLhW2YBr1apVSE5OxrBhw6DVajF69GgsXbrUJDeDwYAVK1ZgwoQJcHBwaOBXgohqYjAor111X4ez3YiOlu+ZOnAA+M1vpH0RiUhdVrmOlT3jOlZElnXiBPDRR+ZjGg3w7ruAt7eqKani9m1pTavycvPx3/8e6NFD3ZyI7JnNrmNFRFQXSsNeHTrYZ1EFSBtJd+kiH+dwIFHjYGFFRDarrAw4eFA+3qePerk0BqXzO3IEuHNHvVyISMLCiohs1pEj0jYv5jg6Kq9Sbg+6dQNcXMzHysuVi04iahgsrIjIZilNWo+MlIbL7JmzMxAVJR/PzlYtFSL6HxZWRGSTSkuBo0fl4/Y+DFhJ6Txzc6V1rYhIPSysiMgmHT0qzbEyx8VF6rFqCjp1AtzdzceEAA4dUjUdoiaPhRUR2aQDB+Rj3bo1nTWcHByAnj3l40qvExFZHgsrIrI59+4pDwMqFRr2SOl8T54ESkrUy4WoqWNhRUQ259gxqbgyx9lZeX0ne9ShA9C8ufmYwQAcPqxuPkRNGQsrIrI5VfZKr6ZbN6m4akq0WuVV1pVeLyKyLBZWRGRTyso4DGiO0ppdubnSFjhE1PBYWBGRTTl2TFpqwRwnp6Y3DFipY0f5dbsqKpSLUSKyHBZWRGRTlIa1IiPlVyK3dw4OyouFcjiQSB0srIjIZpSVSdvYyGmqw4CVlIYDjx+X3/6HiCyHhRUR2YzcXOVhwKayKKicTp0AV1fzsfJyDgcSqYGFFRHZDKVlA7p2bbrDgJUcHYHu3eXjXCyUqOGxsCIim1DTekxKyw00JUrDocePSz1XRNRwWFgRkU3Iy5PfUFir5TBgpc6d5XvuSkulldiJqOGwsCIim6C0mXCHDvJLDTQ1Tk5ScSWHmzITNSwWVkRk9YRQLgiUlhloipRej8OHpdeTiBoGCysisno6HXDtmnxcacJ2UxQZKQ2PmqPXA+fPq5oOUZPCwoqIrJ5Sb1XbtoCPj2qp2AR3d6B9e/k4N2UmajgsrIjI6ikVAuytMk/pdeE8K6KGw8KKiKxaYaF0RaAczq8yT+l1+fln5aFVIqo/FlZEZNWUtrDx9QVat1YvF1tS02vD4UCihsHCioismtKwVffugEajWio2R2k4kIUVUcNgYUVEVuvuXeDUKfk4hwGVKb0+Z88Ct26plgpRk8HCiois1okT8luw1HTlG0lXTHp7m48JoTzMSkT1w8KKiKzW0aPysW7d5NdqIolGw+FAIrXxxxIRWSUhai6sqGZKhVVuLjdlJrI0FlZEZJUuXJDfdNnBQXk/PPpVx46Aq6v5WGkpcPq0uvkQ2TurLKyWLVuG0NBQuLq6Ijo6Gvv27VNsv27dOkRERMDV1RWRkZHYvHmzSVwIgfnz5yMwMBBubm6Ii4vDmTNnTNoUFBQgKSkJnp6e8Pb2xqRJk3DrvpmdQgi8//776NChA1xcXNC6dWu88847ljlpIjKhNP8nPFy+WCBTjo5Ap07ycaVeQSKqO6srrNasWYOUlBQsWLAABw4cQPfu3REfH49rMqvZ7dmzB2PHjsWkSZNw8OBBJCQkICEhAceOHTO2Wbx4MZYuXYrU1FRkZWXB3d0d8fHxuHv3rrFNUlISjh8/jvT0dGzatAk7d+7ElClTTJ5r2rRp+OSTT/D+++/j5MmT2LBhA/r06dMwLwRRE8dhQMuJjJSPHT3KTZmJLEkjhHV9pKKjo9G7d298/PHHAACDwYDg4GBMnToVs2fPrtY+MTERJSUl2LRpk/FY3759ERUVhdTUVAghEBQUhBkzZmDmzJkAgKKiIvj7+2PFihUYM2YMcnNz0blzZ2RnZ6NXr14AgLS0NIwYMQKXL19GUFAQcnNz0a1bNxw7dgwdO3as9/np9Xp4eXmhqKgInp6e9X4cIntWWAi8+qp8/K23AD8/1dKxeXo98Mor8vE33wT8/dXLh8gW1fb3t1X1WN27dw85OTmIi4szHtNqtYiLi0NmZqbZ+2RmZpq0B4D4+Hhj+7y8POh0OpM2Xl5eiI6ONrbJzMyEt7e3sagCgLi4OGi1WmRlZQEANm7ciHbt2mHTpk0ICwtDaGgofvvb36KgoEDxnEpLS6HX601uRKSsSodzNX5+LKrqytMTCAmRj3M4kMhyrKqwunHjBioqKuB/359O/v7+0Ol0Zu+j0+kU21d+ramN330/qR0dHeHj42Ns89NPP+HChQtYt24dPvvsM6xYsQI5OTl45plnFM9p0aJF8PLyMt6Cg4MV2xOR8vwqDgPWT03DgURkGVZVWFkzg8GA0tJSfPbZZxgwYAAGDx6Mf/3rX9i2bRtOKSwNPWfOHBQVFRlvly5dUjFrIttTVgacPCkfVyoQSJ7S63b6NHDnjnq5ENkzqyqsfH194eDggPz8fJPj+fn5CAgIMHufgIAAxfaVX2tqc//k+PLychQUFBjbBAYGwtHRER06dDC26fS/S20uXrwoe04uLi7w9PQ0uRGRvNOnpWUAzHF15Wrr9RUSIg0JmmMwSGtaEdGDs6rCytnZGT179kRGRobxmMFgQEZGBmJiYszeJyYmxqQ9AKSnpxvbh4WFISAgwKSNXq9HVlaWsU1MTAwKCwuRk5NjbLN161YYDAZER0cDAPr374/y8nKcO3fO2Ob0/xaACVGavEBEdaI0LNW5s7R8ANWdRgN07Sof53AgkWVYVWEFACkpKVi+fDlWrlyJ3NxcvPTSSygpKcHEiRMBAOPGjcOcOXOM7adNm4a0tDQsWbIEJ0+exMKFC7F//34kJycDADQaDaZPn463334bGzZswNGjRzFu3DgEBQUhISEBgNTzNHz4cEyePBn79u3D7t27kZycjDFjxiAoKAiANJn94YcfxosvvoiDBw8iJycHv/vd7/DII4+Y9GIRUf3VtNo6hwEfDJddIGp4Vve3X2JiIq5fv4758+dDp9MhKioKaWlpxsnnFy9ehLbKBmH9+vXD6tWrMXfuXLz22msIDw/H+vXr0bXKn2azZs1CSUkJpkyZgsLCQsTGxiItLQ2uVVYYXLVqFZKTkzFs2DBotVqMHj0aS5cuNca1Wi02btyIqVOnYuDAgXB3d8djjz2GJUuWqPCqEDUNOh1w44Z8XKnHhWrWqZO0v6LBUD1WXCytdh8aqnpaRHbF6taxsndcx4pI3pYtwNdfm4+FhgJVOqupnj74AJC73ubxx4EnnlA3HyJbYZPrWBFR08ZhwIantFwF51kRPTgWVkRkFW7fBs6elY+zsLIMpdfxwgVplXYiqj8WVkRkFXJzzc/9AaRlAtq2VTcfe+XnB7RqJR9nrxXRg2FhRURW4fhx+VhkpLRcAD04jYarsBM1JBZWRNTohFAurHg1oGUpFVa5uUBFhXq5ENkbFlZE1OiuXgUKC83HtFogIkLVdOxehw6As7P52N27wE8/qZsPkT1hYUVEjU6pt6pdO6BZM/VyaQocHZWLVaX3g4iUsbAiokZ37Jh8jMOADaNLF/kYCyui+mNhRUSN6u5d5WUWlAoAqj+lgvXiRS67QFRfLKyIqFGdOiU/WdrDAwgOVjefpsLXV1p6Qc6JE+rlQmRPWFgRUaNSGnbq0oXLLDQkDgcSWR4LKyJqNEIoz6/iMGDDUhoOPH5cfsFWIpLHwoqIGs21a8DNm+ZjGg3QubO6+TQ14eHSFYLmlJRIc62IqG5YWBFRo1HqrQoJAZo3Vy+XpsjFRSqu5Ci9P0RkHgsrImo0XG298dU0HEhEdcPCiogaRVkZcPq0fJzzq9Sh9Drn5UlDgkRUeyysiKhRnD4tFVfmNGsGhIaqmk6TFRAA+PiYjwkh7R1IRLXHwoqIGoXSMFPnztIegdTwNBouu0BkSfzRRUSNoqb1q0g9NRVWQqiXC5GtY2FFRKq7eRPQ6eTjLKzUFREh30NYVARcuaJuPkS2jIUVEalOqbeqTRvAy0u9XAhwcwMeekg+zuFAotpjYUVEquNq69ZHadkFrmdFVHssrIhIVeXlwMmT8nGuX9U4lAras2eBu3fVy4XIlrGwIiJV/fQTUFpqPubqCrRrp24+JGnTBvD0NB8zGIBTp9TNh8hWsbAiIlUpDStFRMjvXUcNq6ZlFzgcSFQ7LKyISFVcZsF6cdkFogfHwoqIVFNYCFy+LB9nYdW4OneWeq7MuXkTyM9XNx8iW8TCiohUc+KEfCwgAGjZUr1cqDp3d+WthLjsAlHNWFgRkWqUfjHzakDrwO1tiB4MCysiUoXBoLyhb+fO6uVC8pQKK6WNs4lIwsKKiFRx8SJQUmI+5uQEdOigbj5kXmgo0KyZ+VhZGXDmjKrpENkcqy2sli1bhtDQULi6uiI6Ohr79u1TbL9u3TpERETA1dUVkZGR2Lx5s0lcCIH58+cjMDAQbm5uiIuLw5n7fkIUFBQgKSkJnp6e8Pb2xqRJk3Dr1i1j/Pz589BoNNVue/futdyJE9kppWGk8HCpuKLGp9Uq9x5yOJBImVUWVmvWrEFKSgoWLFiAAwcOoHv37oiPj8e1a9fMtt+zZw/Gjh2LSZMm4eDBg0hISEBCQgKOVVl4ZfHixVi6dClSU1ORlZUFd3d3xMfH426V5YSTkpJw/PhxpKenY9OmTdi5cyemTJlS7fl++OEH/Pzzz8Zbz549Lf8iENkZLrNgOzjPiqj+NEJY38ok0dHR6N27Nz7++GMAgMFgQHBwMKZOnYrZs2dXa5+YmIiSkhJs2rTJeKxv376IiopCamoqhBAICgrCjBkzMHPmTABAUVER/P39sWLFCowZMwa5ubno3LkzsrOz0atXLwBAWloaRowYgcuXLyMoKAjnz59HWFgYDh48iKioqHqdm16vh5eXF4qKiuApt8wxkZ25fRuYMUOaZ2XOwoVAYKCqKZGCwkLg1Vfl44sWAT4+qqVDZBVq+/vb6nqs7t27h5ycHMTFxRmPabVaxMXFITMz0+x9MjMzTdoDQHx8vLF9Xl4edDqdSRsvLy9ER0cb22RmZsLb29tYVAFAXFwctFotsrKyTB77ySefhJ+fH2JjY7FhwwbF8yktLYVerze5ETU1J0/KF1UtWkhLLZD18PYGWreWj7PXikie1RVWN27cQEVFBfz9/U2O+/v7Q6fTmb2PTqdTbF/5taY2fn5+JnFHR0f4+PgY2zRv3hxLlizBunXr8N133yE2NhYJCQmKxdWiRYvg5eVlvAUHB9f0EhDZHaX1q5QWpaTGozQcqPR+EjV13JWrDnx9fZGSkmL8f+/evXH16lX85S9/wZNPPmn2PnPmzDG5j16vZ3FFTYoQnF9li7p0AbZsMR/LzZV6ILVW96c5UeOzuo+Fr68vHBwckH/f3gn5+fkIkBkvCAgIUGxf+bWmNvdPji8vL0dBQYHs8wLSfLCzZ8/Kxl1cXODp6WlyI2pK8vOBggLzMY0G6NRJ3Xyodtq3B5ydzcfu3AHy8tTNh8hWWF1h5ezsjJ49eyIjI8N4zGAwICMjAzExMWbvExMTY9IeANLT043tw8LCEBAQYNJGr9cjKyvL2CYmJgaFhYXIyckxttm6dSsMBgOio6Nl8z106BACOeuWSJZSb1VYmPyaSdS4HB2Bjh3l41UuuiaiKqxyKDAlJQXjx49Hr1690KdPH3z44YcoKSnBxIkTAQDjxo1D69atsWjRIgDAtGnTMGjQICxZsgQjR47El19+if379+Of//wnAECj0WD69Ol4++23ER4ejrCwMMybNw9BQUFISEgAAHTq1AnDhw/H5MmTkZqairKyMiQnJ2PMmDEICgoCAKxcuRLOzs7o0aMHAOCbb77Bv//9b3zyyScqv0JEtqOm+VVkvbp0AY4eNR87fhwYNUrdfIhsgVUWVomJibh+/Trmz58PnU6HqKgopKWlGSefX7x4Edoqg/v9+vXD6tWrMXfuXLz22msIDw/H+vXr0bXK5mOzZs1CSUkJpkyZgsLCQsTGxiItLQ2urq7GNqtWrUJycjKGDRsGrVaL0aNHY+nSpSa5vfXWW7hw4QIcHR0RERGBNWvW4JlnnmngV4TINpWVAadOycc5v8q6Kb0/Fy8CxcWAh4d6+RDZAqtcx8qecR0rakpyc4EPPzQfa9YMWLKEE6Ct3euvAzdumI9NmgT06aNuPkSNxWbXsSIi+6E0DBgRwaLKFlTp+K+G61kRVccfa0TUYLjMgu2raT0rjnkQmWJhRUQNorAQuHJFPs7CyjZ07Ag4OJiP6fXA5cvq5kNk7VhYEVGDUBoGDAyUtrIh6+fiIq1pJYfDgUSmWFgRUYPgMgv2Q6l3kYUVkSkWVkRkcQaDcmHFYUDbovR+nT0L3L2rXi5E1o6FFRFZ3MWLQEmJ+ZijIxAerm4+9GBatwbkri43GJTXKiNqalhYEZHFKfVWhYfL70FH1kmjUe614vY2RL9iYUVEFqc070ZpXSSyXjXNs+KyC0QSFlZEZFF37gA//SQf58R129S5s9RzZc7Nm8C1a+rmQ2StWFgRkUWdPCnNuzHH21taaoFsj7s7EBIiH+fVgUQSFlZEZFE1rbYu1+tB1o/b2xDVjIUVEVmMEFy/yp4pzbM6dQooK1MvFyJrxcKKiCzm2jVpvo05Gg3QqZO6+ZBlhYYCzZqZj5WVSWtaETV1LKyIyGKUhoNCQ6V5OmS7tFrl4pjDgUQsrIjIgmqaX0W2j9vbECljYUVEFlFeDpw+LR/n/Cr7oPQ+Xr0K/PKLerkQWSMWVkRkEWfPAvfumY+5uQFhYermQw2jRQsgKEg+rnTxAlFTwMKKiCxCaRioUydpfg7ZB25vQySPP+qIyCK4zELToVRYKS0QS9QUsLAiogdWVARcviwf58R1+9K+vfxG2rdvA3l56uZDZE3qXFilpKRgy5YtDZELEdkopd6qgADAx0e9XKjhOTkBHTrIxznPipqyOhdWH374Ifbu3Wty7L333kPLli0tlhQR2RYus9D0KG1vw3lW1JRZZCjw7t27KCwstMRDEZGNEQLIzZWPc36VfVIqmC9cAG7dUi8XImvCOVZE9EAuXpT/JeroqDxkRLarVSvA19d8rKZim8iesbAiogeiNOwTHi4/yZlsm0bDVdiJzGFhRUQPRKmw4vwq+1ZTYSWEerkQWQvH+tzp8uXL2Ldvn8n/ASA7OxtC5pPUp0+f+jwVEVmxkhLlS+uVJjiT7evYUVr41dy6VXo9cOUK0KaN+nkRNaZ6FVb/+te/8K9//cvkmBACffv2lb1PRUVFfZ6KiKzYiRPyvRI+PtJSC2S/XF2lNa3k9og8fpyFFTU9dS6sxo8f3xB5EJENqmkYUKNRLxdqHF26KBdW8fHq5kPU2OpcWH366acNkQcR2RghlCcocxiwaejSBfjvf83Hzp4F7t6VeraImgqrnby+bNkyhIaGwtXVFdHR0SZzusxZt24dIiIi4OrqisjISGzevNkkLoTA/PnzERgYCDc3N8TFxeHMmTMmbQoKCpCUlARPT094e3tj0qRJuCVzHfnZs2fh4eEBb2/vBzpPIlt18SJQXGw+5uAARESomw81jjZtAE9P87GKCuDUKXXzIWpsD1xYFRcXY/v27fjqq6/w1VdfYceOHSiW+2lbS2vWrEFKSgoWLFiAAwcOoHv37oiPj8e1a9fMtt+zZw/Gjh2LSZMm4eDBg0hISEBCQgKOVRmnWLx4MZYuXYrU1FRkZWXB3d0d8fHxuHv3rrFNUlISjh8/jvT0dGzatAk7d+7ElClTqj1fWVkZxo4diwEDBjzQeRLZMqXeqvbt2UvRVGg0yovAcnsbamo0Qu4yvhocO3YMs2fPxvfffw/DfZeEODg4YMSIEfjzn/+MzvVYdjk6Ohq9e/fGxx9/DAAwGAwIDg7G1KlTMXv27GrtExMTUVJSgk2bNhmP9e3bF1FRUUhNTYUQAkFBQZgxYwZmzpwJACgqKoK/vz9WrFiBMWPGIDc3F507d0Z2djZ69eoFAEhLS8OIESNw+fJlBAUFGR/71VdfxdWrVzFs2DBMnz69TqvO6/V6eHl5oaioCJ5yf+YR2YDFi4Fz58zHRo8GHn1U3Xyo8WRnA598Yj7m6wu88466+RA1hNr+/q5Xj9WOHTvQr18/bN68GS4uLoiNjcVzzz2H5557DrGxsXB2dsaGDRvQr18/7N69u06Pfe/ePeTk5CAuLu7XJLVaxMXFITMz0+x9MjMzTdoDQHx8vLF9Xl4edDqdSRsvLy9ER0cb22RmZsLb29tYVAFAXFwctFotsrKyjMe2bt2KdevWYdmyZXU6LyJ7UlIC/PSTfJzzq5qWTp3kL1S4cQOQGWwgskt1nrx++/ZtvPDCC7h9+zYWLlyIGTNmwN3d3aRNSUkJ3n//fbz11lt4/vnnkZubC9dajgvcuHEDFRUV8Pf3Nznu7++PkydPmr2PTqcz216n0xnjlceU2vj5+ZnEHR0d4ePjY2xz8+ZNTJgwAZ9//nmte5tKS0tRWlpq/L9er6/V/YisWW6u/DILLVoAgYHq5kONq3lzICQEOH/efPz4ceC+H69EdqvOPVZr167F5cuXsWjRIsyfP79aUQUA7u7uWLBgAf785z/j4sWLWLdunUWSbWyTJ0/Gb37zGwwcOLDW91m0aBG8vLyMt+Dg4AbMkEgdSsssdO3KZRaaIm5vQySpc2G1efNmtGrVCtOnT6+x7fTp09GyZUuTuU818fX1hYODA/Lz802O5+fnI0BmtcGAgADF9pVfa2pz/+T48vJyFBQUGNts3boV77//PhwdHeHo6IhJkyahqKgIjo6O+Pe//202tzlz5qCoqMh4u3TpUm1eBiKrVdMyC9zGpmlSet9PnQLKy9XLhagx1bmwOnz4MAYMGAAnJ6ca2zo7O2PgwIE4dOhQrR/f2dkZPXv2REZGhvGYwWBARkYGYmJizN4nJibGpD0ApKenG9uHhYUhICDApI1er0dWVpaxTUxMDAoLC5GTk2Nss3XrVhgMBkRHRwOQ5mEdOnTIeHvzzTfh4eGBQ4cO4amnnjKbm4uLCzw9PU1uRLbs8mVpuxJztFppvg01PWFhgJub+di9e9KaVkRNQZ3nWF27dg2hoaG1bh8WFlat6KlJSkoKxo8fj169eqFPnz748MMPUVJSgokTJwIAxo0bh9atW2PRokUAgGnTpmHQoEFYsmQJRo4ciS+//BL79+/HP//5TwCARqPB9OnT8fbbbyM8PBxhYWGYN28egoKCkJCQAADo1KkThg8fjsmTJyM1NRVlZWVITk7GmDFjjFcEdrrvN8b+/fuh1WrRlTN1qQlRGgbkMgtNV2VRfeCA+fjx41zbjJqGOhdWxcXFdep1ad68uewim3ISExNx/fp1zJ8/HzqdDlFRUUhLSzNOPr948SK02l872/r164fVq1dj7ty5eO211xAeHo7169ebFDyzZs1CSUkJpkyZgsLCQsTGxiItLc1kUv2qVauQnJyMYcOGQavVYvTo0Vi6dGmdcieydzXNr6Kmq0sX5cJq9Gh18yFqDHVex0qr1WLhwoWYP39+rdq/8cYbePPNN7kJ8/9wHSuyZbdvAzNmAPctXWc0fz7QurW6OZH1+OUXwMxSg0bvvQdwswqyVbX9/V3nHitAWhx07dq1tW5LRPYhN1e+qPL2Bqqso0tNUIsW0vfA1avm4ydOAP36qZsTkdrqVVh9/fXX+Prrr2vVVggBDa+9JrILXGaBatK5s3xhdewYCyuyf3UurBYsWNAQeRCRlatpmQXOryJA+j744QfzsRMnpI2ZHRzUzYlITSysiKhWLl8GiorMx7jMAlVq3x5wcgLKyqrH7tyR9pfs0EH9vIjUUq+9AjMzMzF06FB4eHjA09MTjzzyCPbt22fp3IjIihw5Ih/jMgtUyclJuchW+j4isgd1LqyOHj2KoUOHYvv27SgpKcGtW7eQkZGBIUOG4Dj3LSCyW0ePysc4DEhVdesmH1P6PiKyB3UurN59912Ulpbi9ddfh06ng06nw7x583Dnzh289957DZEjETUyvV5+g11A+RcpNT2RkfIxnQ64b/cwIrtS58Jq165diI2NxVtvvQU/Pz/4+fnhjTfewIABA7Bjx46GyJGIGtmxY9LkdXN8fQGZbTypifL2BpT2m2evFdmzOhdW+fn56Nu3b7Xj0dHR1TY5JiL7oPSLMDKSyyxQdUq9ViysyJ7VubAqKytD8+bNqx13d3dHmbnLQIjIppWXKy+zwGFAMkfp++L0aeDuXfVyIVJTva4KJKKm48wZoLTUfMzFhZfOk3mhoYCHh/lYRYW0ij+RParXyuuff/459u7da3Ls7NmzAIARI0ZUa6/RaPDdd9/V56mIqJEpDdt07gw41uunCNk7jUa6WjQz03z8yBGgRw91cyJSQ71+JJ49e9ZYSN0vLS2t2jFuaUNkm4RQXndIaR4NUbdu8oXV0aPS9xd/PZC9qXNhlZeX1xB5EJEVunYNuH5dPs71q0hJ587SqvzmNu4uLgYuXJCGDInsSZ0Lq5CQkIbIg4iskFJvVUgI4OWlXi5ke1xdpTl4J0+ajx89ysKK7A8nrxORLKXCilcDUm0oDRdzexuyRyysiMis27cBmamUADi/impHqQC/eBEoLFQtFSJVsLAiIrNOnDA/NwaQhgDbtlU3H7JNfn7STc6xY+rlQqQGFlZEZFZNVwPyai6qLaVeKw4Hkr1hYUVE1RgMyj0JHAakulD6fsnNBbhpB9kTFlZEVM25c0BJifmYoyPQqZO6+ZBta99eukLQnHv3gFOn1M2HqCGxsCKiag4flo916CBtZUNUW46O0ppWcg4dUi0VogbHwoqITAih/Iuue3fVUiE7ovR9c/iw9H1HZA9YWBGRiZ9/Vl5tnYUV1UdkpLQKuzl6PcBNPchesLAiIhNKvVUhIUCLFqqlQnbE3R0ID5ePcziQ7AULKyIyoTS/KipKtTTIDtU0HEhkD1hYEZFRYSFw/rx8nIUVPQil7x+dDsjPVy0VogbDwoqIjJR6DXx9gcBA9XIh+9OyJdCmjXycw4FkD1hYEZGR0i+2qCiutk4PTqnXioUV2QMWVkQEALhzR3mhRg4DkiUofR/l5UlXCBLZMhZWRARA2sKmosJ8rHlz4KGH1M2H7FObNoCPj/mYEJzETrbPagurZcuWITQ0FK6uroiOjsa+ffsU269btw4RERFwdXVFZGQkNm/ebBIXQmD+/PkIDAyEm5sb4uLicObMGZM2BQUFSEpKgqenJ7y9vTFp0iTcunXLGD916hSGDBkCf39/uLq6ol27dpg7dy7KuNEV2QGlX2jdusmvQURUFxoNrw4k+2aVPyrXrFmDlJQULFiwAAcOHED37t0RHx+Pa9eumW2/Z88ejB07FpMmTcLBgweRkJCAhIQEHKuyi+zixYuxdOlSpKamIisrC+7u7oiPj8fdu3eNbZKSknD8+HGkp6dj06ZN2LlzJ6ZMmWKMOzk5Ydy4cdiyZQtOnTqFDz/8EMuXL8eCBQsa7sUgUkF5OXD0qHycw4BkSUrfT7m5QGmpaqkQWZxGCOvbSCA6Ohq9e/fGxx9/DAAwGAwIDg7G1KlTMXv27GrtExMTUVJSgk2bNhmP9e3bF1FRUUhNTYUQAkFBQZgxYwZmzpwJACgqKoK/vz9WrFiBMWPGIDc3F507d0Z2djZ69eoFAEhLS8OIESNw+fJlBAUFmc01JSUF2dnZ2LVrV63OTa/Xw8vLC0VFRfD09KzT60LUUE6cAD76yHzMyQn44APA2VndnMh+VVQAM2cCt2+bj//ud8DDD6ubE1FNavv72+p6rO7du4ecnBzExcUZj2m1WsTFxSEzM9PsfTIzM03aA0B8fLyxfV5eHnQ6nUkbLy8vREdHG9tkZmbC29vbWFQBQFxcHLRaLbKyssw+79mzZ5GWloZBgwbV72SJrMTBg/Kxzp1ZVJFlOThIW9zI4dWBZMusrrC6ceMGKioq4O/vb3Lc398fOp3O7H10Op1i+8qvNbXx8/MziTs6OsLHx6fa8/br1w+urq4IDw/HgAED8Oabb8qeT2lpKfR6vcmNyJoYDDUvs0BkaUrfV4cPS8PTRLbI6gorW7BmzRocOHAAq1evxnfffYf3339ftu2iRYvg5eVlvAUHB6uYKVHNzp2Tv8Rdo1HuWSCqr86dAUdH87G7d6W5VkS2yOoKK19fXzg4OCD/vr0N8vPzERAQYPY+AQEBiu0rv9bU5v7J8eXl5SgoKKj2vMHBwejcuTPGjh2Ld999FwsXLkSFzHXqc+bMQVFRkfF26dIlpdMnUl1OjnysY0fAw0O9XKjpcHUFunSRjx84oF4uRJZkdYWVs7MzevbsiYyMDOMxg8GAjIwMxMTEmL1PTEyMSXsASE9PN7YPCwtDQECASRu9Xo+srCxjm5iYGBQWFiKnym+ZrVu3wmAwIDo6WjZfg8GAsrIyGAwGs3EXFxd4enqa3IishRDK86t69FAvF2p6evaUjx06xOFAsk0yHbGNKyUlBePHj0evXr3Qp08ffPjhhygpKcHEiRMBAOPGjUPr1q2xaNEiAMC0adMwaNAgLFmyBCNHjsSXX36J/fv345///CcAQKPRYPr06Xj77bcRHh6OsLAwzJs3D0FBQUhISAAAdOrUCcOHD8fkyZORmpqKsrIyJCcnY8yYMcYrAletWgUnJydERkbCxcUF+/fvx5w5c5CYmAgnJyf1XyiiB5SXJ228bI5Gw8KKGla3btJEdnMd/rdvSzsBKPVqEVkjqyysEhMTcf36dcyfPx86nQ5RUVFIS0szTj6/ePEitFVWK+zXrx9Wr16NuXPn4rXXXkN4eDjWr1+Prl27GtvMmjULJSUlmDJlCgoLCxEbG4u0tDS4uroa26xatQrJyckYNmwYtFotRo8ejaVLlxrjjo6OeO+993D69GkIIRASEoLk5GT86U9/UuFVIbI8pWHA9u0BLy/1cqGmx81Nmmslt4bagQMsrMj2WOU6VvaM61iRtRACeP114OZN8/HnngOGDVM3J2p69uwBVq40H3N3B95/n6v+k3Ww2XWsiEgdFy/KF1UAF2gkdXTvLl84lZQAp0+rmw/Rg2JhRdREKQ0DtmsHtGihXi7UdLm7A506yceVvk+JrBELK6ImSAjly9k5aZ3UpNQ7evCgtIgtka1gYUXUBF25Aly/Lh/nMCCpKSpKfjiwuBg4e1bVdIgeCAsroiZIaXilbVvA11e9XIiaNwc6dJCPc7FQsiUsrIiaGCGA/fvl4+ytosagtFjogQPS9y2RLWBhRdTEXLwI3Ld7kwkWVtQYoqKkRWnNKSricCDZDhZWRE2MUm9VcDDwv3V4iVTl6QmEh8vHs7PVy4XoQbCwImpChFD+BdW7t3q5EN1PaTgwJ8f81jdE1oaFFVETcu4c8Msv8vFevdTLheh+Dz8sf3XgrVtAbq66+RDVBwsroiZEqbfqoYeAli3Vy4Xofp6eQESEfJzDgWQLWFgRNREGg/IyCxwGJGug9H148CBQVqZeLkT1wcKKqIk4eVJabNEcjUZ5fguRWnr0ABwdzcdKS4GjR9XNh6iuWFgRNRFKwygREdIwDFFjc3MDIiPl4/v2qZcLUX2wsCJqAsrLpWEUORwGJGui9P149Chw5456uRDVFQsroibg+HH5X0YODtx0maxLt26Ai4v5WE1/JBA1NhZWRE2A0vBJ165As2bq5UJUEycn5WKfVweSNWNhRWTnbt8GDh2Sj3MYkKyR0vflyZOAXq9eLkR1wcKKyM4dOCANn5jj7CwNuxBZm06dAHd38zGDgb1WZL1YWBHZub175WM9esjPZSFqTA4OykuAZGaqlwtRXbCwIrJjN24AZ87Ix2Ni1MuFqK769pWPXboEXLmiXi5EtcXCisiOKfVWeXsDHTuqlgpRnbVrB/j5ycfZa0XWiIUVkZ0SQvkXT3S0/Ia3RNZAo1HutcrKkuZbEVkT/lglslM//SQNBcpR+oVFZC2Uvk/1euDECfVyIaoNFlZEdkqpt6ptWyAoSL1ciOqrZUugQwf5OIcDydqwsCKyQ2VlwP798nH2VpEtUbrI4tAhaa02ImvBworIDh0+LL+FjVYL9Omjbj5ED+Lhh6U118wpLwdyctTNh0gJCysiO/Tjj/Kxrl0BDw/1ciF6UK6uylvc7NmjXi5ENWFhRWRnbtwAcnPl4xwGJFukNBz400/A1avq5UKkhIUVkZ3ZvVs+1rw50L27erkQWUrHjkCLFvJxpV5aIjWxsCKyIwaD8rBI376Ao6N6+RBZilar3Gu1d6900QZRY7PawmrZsmUIDQ2Fq6sroqOjsW/fPsX269atQ0REBFxdXREZGYnNmzebxIUQmD9/PgIDA+Hm5oa4uDicuW+vj4KCAiQlJcHT0xPe3t6YNGkSbt26ZYxv374do0aNQmBgINzd3REVFYVVq1ZZ7qSJHtCxY0BhoXw8Nla1VIgsLjZWWjTUnJIS4OBBdfMhMscqC6s1a9YgJSUFCxYswIEDB9C9e3fEx8fj2rVrZtvv2bMHY8eOxaRJk3Dw4EEkJCQgISEBx44dM7ZZvHgxli5ditTUVGRlZcHd3R3x8fG4e/eusU1SUhKOHz+O9PR0bNq0CTt37sSUKVNMnqdbt274+uuvceTIEUycOBHjxo3Dpk2bGu7FIKoDpeGQhx4CAgPVy4XI0lq2BDp1ko/v2qVeLkRyNEII0dhJ3C86Ohq9e/fGxx9/DAAwGAwIDg7G1KlTMXv27GrtExMTUVJSYlLg9O3bF1FRUUhNTYUQAkFBQZgxYwZmzpwJACgqKoK/vz9WrFiBMWPGIDc3F507d0Z2djZ69eoFAEhLS8OIESNw+fJlBMmspjhy5Ej4+/vj3//+d63OTa/Xw8vLC0VFRfD09KzT60KkpLAQmDNHfouP8eOBfv1UTYnI4g4cAP7xD/n4W28p7y9IVF+1/f1tdT1W9+7dQ05ODuLi4ozHtFot4uLikCmzxG5mZqZJewCIj483ts/Ly4NOpzNp4+XlhejoaGObzMxMeHt7G4sqAIiLi4NWq0VWVpZsvkVFRfDx8an7iRJZWGamfFHl6gr07KluPkQNoVs35eVCOImdGpvVFVY3btxARUUF/P39TY77+/tDp9OZvY9Op1NsX/m1pjZ+9/2Z4+joCB8fH9nnXbt2LbKzszFx4kTZ8yktLYVerze5EVmaEMq/UPr0AVxc1MuHqKE4Oir3vO7ZIy0aStRYrK6wshXbtm3DxIkTsXz5cnTp0kW23aJFi+Dl5WW8BQcHq5glNRXHjytvuMxJ62RPlL6fi4ulnQeIGovVFVa+vr5wcHBAfn6+yfH8/HwEBASYvU9AQIBi+8qvNbW5f3J8eXk5CgoKqj3vjh078MQTT+D//b//h3Hjximez5w5c1BUVGS8Xbp0SbE9UX1s2yYfa9NG2nSZyF74+SlvzLx9u2qpEFVjdYWVs7MzevbsiYyMDOMxg8GAjIwMxMgsYhITE2PSHgDS09ON7cPCwhAQEGDSRq/XIysry9gmJiYGhYWFyKmy6dTWrVthMBgQHR1tPLZ9+3aMHDkS7733nskVg3JcXFzg6elpciOypOvXpR4rOYMGyV+iTmSrBgyQj50+DVy5ol4uRFVZXWEFACkpKVi+fDlWrlyJ3NxcvPTSSygpKTHOZRo3bhzmzJljbD9t2jSkpaVhyZIlOHnyJBYuXIj9+/cjOTkZAKDRaDB9+nS8/fbb2LBhA44ePYpx48YhKCgICQkJAIBOnTph+PDhmDx5Mvbt24fdu3cjOTkZY8aMMV4RuG3bNowcORJ//OMfMXr0aOh0Ouh0OhQUFKj7AhFVsWOHNMfKHFdXoMrfBUR2o0cP5UnsSr24RA3JKgurxMREvP/++5g/fz6ioqJw6NAhpKWlGSefX7x4ET///LOxfb9+/bB69Wr885//RPfu3fHVV19h/fr16Nq1q7HNrFmzMHXqVEyZMgW9e/fGrVu3kJaWBldXV2ObVatWISIiAsOGDcOIESMQGxuLf/7zn8b4ypUrcfv2bSxatAiBgYHG29NPP63Cq0JU3b17ylvY9OvHSetkn5yclOdaZWUBt2+rlw9RJatcx8qecR0rsqTdu4HPPpOPv/kmcN/FsER245dfpLXb5H6LPfsscN9KPET1ZrPrWBFR7QihPNzRqROLKrJvLVoAUVHy8e3b5YsuoobCworIRv30E6B0kemQIerlQtRYlL7Pa7qwg6ghsLAislH3XQhrwscHiIxULxeixtKhAyCz4xgAYOtW9XIhAlhYEdmkGzekPdPkDBoEaPnppiZAo1HutTp+HKhyrRNRg+OPXiIbtHWr/NwRR0egf3918yFqTNHR0tIictLT1cuFiIUVkY25fVt5X8C+fZXX9yGyNy4uyn9MZGUBRUXq5UNNGwsrIhuzaxdQWiof5+Xl1BQNHSq/w0B5ORcMJfWwsCKyIeXlypNxu3YFAgPVy4fIWvj6Aj17ysd37FD+g4TIUlhYEdmQnBygsFA+/sgjqqVCZHUefVQ+VtMQOpGlsLAishFCAGlp8vHgYKBjR/XyIbI2ISHS8gtyMjIAg0G9fKhpYmFFZCOOHAGuXpWPP/KI/BwToqYiPl4+dvOm1OtL1JBYWBHZACGA776Tj3t7K88vIWoqunRRXjB082Zuc0MNi4UVkQ3IzQUuXJCPP/qotH4VUVOn0SjPNbx6FTh0SLV0qAliYUVkAzZvlo81bw7ExqqXC5G169NH6sWV89137LWihsPCisjKnT0LnDkjH4+LkxZIJCKJo6PyFYKXLgFHj6qXDzUtLKyIrJzS3Co3N2DwYNVSIbIZAwYo70CwaRN7rahhsLAismJnzgAnTsjHhwyRiisiMuXsrNxrdeGCtEEzkaWxsCKyUkIA334rH3d2BoYNUy8fIlszaJA0B1HOhg3stSLLY2FFZKVOnFCeWzV4sPIvDaKmzsVFee/MCxeAgwfVy4eaBhZWRFaopt4qFxflYQ4ikgwZAjRrJh//9luuxk6WxcKKyAodPqy8btWwYcoTc4lI4uqqvK6VTgdkZqqXD9k/FlZEVsZgUO6tataMmy0T1cWwYYCnp3x840agrEy9fMi+sbAisjK7dyvvCfjoo8pDG0RkysUFGDFCPv7LL8COHerlQ/aNhRWRFbl7V7m3ysMDGDpUvXyI7MWAAUDLlvLxzZuBkhL18iH7xcKKyIqkpQHFxfLxxx7jKutE9eHoCDz5pHy8pERaNJToQbGwIrISv/wC/PCDfLxVK2ldHiKqnz59gKAg+fj27cDPP6uWDtkpFlZEVuK//1WeQPv009Jf3URUP1qt9DmSYzAAX32lXj5kn1hYEVmBs2eBrCz5ePv2QI8e6uVDZK+6dgU6d5aPHzsm3Yjqi4UVUSMzGIDVq5XbPPssoNGokw+RPdNopM+TVuG339q1QHm5ejmRfWFhRdTItm4FrlyRj/fpA4SGqpYOkd0LCgIGDpSP5+cDW7aolw/ZFxZWRI2osFBanFCOkxOQkKBWNkRNx5NPKq8H9913wLVr6uVD9oOFFVEj+uorae0qOSNHKq+9Q0T14+4OPP64fLy8HPjiC2nfTqK6sMrCatmyZQgNDYWrqyuio6Oxb98+xfbr1q1DREQEXF1dERkZic2bN5vEhRCYP38+AgMD4ebmhri4OJw5c8akTUFBAZKSkuDp6Qlvb29MmjQJt27dMsbv3r2LCRMmIDIyEo6OjkhgNwI9oKNHgexs+bi/P7euIWpIgwcDbdrIx0+cAPbvVy0dshNWV1itWbMGKSkpWLBgAQ4cOIDu3bsjPj4e12T6ZPfs2YOxY8di0qRJOHjwIBISEpCQkIBjVS7rWLx4MZYuXYrU1FRkZWXB3d0d8fHxuFulqyApKQnHjx9Heno6Nm3ahJ07d2LKlCnGeEVFBdzc3PDHP/4RcXFxDfcCUJNw+zbw+efKbX7zGy6vQNSQHByApCTlC0PWruWK7FQ3GiGsq6MzOjoavXv3xscffwwAMBgMCA4OxtSpUzF79uxq7RMTE1FSUoJNVZbM7du3L6KiopCamgohBIKCgjBjxgzMnDkTAFBUVAR/f3+sWLECY8aMQW5uLjp37ozs7Gz06tULAJCWloYRI0bg8uXLCLpvRbkJEyagsLAQ69evr/P56fV6eHl5oaioCJ5Ku4KSXfvsM2lPQDm9ewO//a16+RA1ZatWATt3ysf5eSSg9r+/rarH6t69e8jJyTHpEdJqtYiLi0NmZqbZ+2RmZlbrQYqPjze2z8vLg06nM2nj5eWF6OhoY5vMzEx4e3sbiyoAiIuLg1arRZbS4kK1UFpaCr1eb3Kjpu34ceWiytUVeOYZ9fIhauqeegpQ+js3OxvIyVEvH7JtVlVY3bhxAxUVFfD39zc57u/vD51OZ/Y+Op1OsX3l15ra+Pn5mcQdHR3h4+Mj+7y1tWjRInh5eRlvwcHBD/R4ZNvu3AH+8x/lNs88A3h7q5IOEUG6OvC555TbrFoF8O9iqg2rKqzs0Zw5c1BUVGS8Xbp0qbFTokYihPTD+Zdf5Nt06gTExqqXExFJevUCIiPl4yUl0rxI65o8Q9bIqgorX19fODg4ID8/3+R4fn4+AgICzN4nICBAsX3l15ra3D85vry8HAUFBbLPW1suLi7w9PQ0uVHTlJWlfBWgiwvwwgtcYZ2oMWg00udPaW2rw4eBXbvUy4lsk1UVVs7OzujZsycyMjKMxwwGAzIyMhATE2P2PjExMSbtASA9Pd3YPiwsDAEBASZt9Ho9srKyjG1iYmJQWFiInCqD6Fu3boXBYEB0dLTFzo+armvXat62ZvRorllF1Ji8vKSrcZWsWQNcvqxOPmSbrKqwAoCUlBQsX74cK1euRG5uLl566SWUlJRg4sSJAIBx48Zhzpw5xvbTpk1DWloalixZgpMnT2LhwoXYv38/kpOTAQAajQbTp0/H22+/jQ0bNuDo0aMYN24cgoKCjGtRderUCcOHD8fkyZOxb98+7N69G8nJyRgzZozJFYEnTpzAoUOHUFBQgKKiIhw6dAiHDh1S7bUh21ReDnzyCVBaKt+mY0flLTaISB29egEPPywfLy8Hli9X/jxT02Z1q+QkJibi+vXrmD9/PnQ6HaKiopCWlmacfH7x4kVoq+ye2a9fP6xevRpz587Fa6+9hvDwcKxfvx5du3Y1tpk1axZKSkowZcoUFBYWIjY2FmlpaXB1dTW2WbVqFZKTkzFs2DBotVqMHj0aS5cuNcltxIgRuHDhgvH/PXr0ACAtQEokZ906oMq3TTXu7sDEiRwCJLIGGo3Ua3XmDFBcbL6NTietyj5hgqqpkY2wunWs7B3XsWpaMjOBFSuU27z0EhAVpUY2RFRbx44Bf/2rcpukJPY0NyU2uY4VkT25eFG6ClDJwIEsqoisUdeuQHy8cpsvvpB6toiqYmFF1ABu3QJSU4GyMvk2gYHAs8+qlxMR1c2oUUC7dvJxgwH4xz+AggL1ciLrx8KKyMLKyoBly4CbN+XbuLgAv/sd4OysXl5EVDcODtJWNkpLMBQXA3/7Gyez069YWBFZkBDAv/8N/PSTcrsJE6QeKyKybi1bSheXKLl0SbpS0GBQJyeybiysiCzoq6+AAweU28THK1/OTUTWpVs3aVhQydGjXJmdJCysiCxkyxbghx+U23TqBPxv+TQisiGPPVbzH0S7dwMbNqiTD1kvFlZEFrB9O/D118pt/P2ByZMBLT91RDZHo5GG8Nu0UW63eXPNf2CRfeOPeKIHtHu3dNm1Eg8PYOpUaTFQIrJNLi7AH/4A1LQE4bp1wH07rVETwsKK6AHs2QP85z/KbZycgJdfBlq1UicnImo4LVsCf/wjUGXjDrPWrmVx1VSxsCKqp4wMYOVK5cmqGg0waRIQFqZeXkTUsIKDpR0THByU261dC3z/PSe0NzUsrIjqSAhg40bph2ZNXngB+N+WkkRkRyIigBdfrHmPz2++ka4WZnHVdLCwIqqDigpg9Wpg06aa244dC/Tv3/A5EVHj6NVL+uOpJj/8IK1vV17e8DlR43Ns7ASIbMXt29L2FSdP1tz2mWeAwYMbPCUiamT9+0sLg37+uXK7ffuAX36Rdlzw8FAnN2oc7LEiqoX8fODdd2tXVD39NPDIIw2fExFZhwEDgOefr7ndmTPAn/8srdRO9ouFFVENsrOBd96RiislGg2QlCStrE5ETcuAAcC4cTXPuSooAN57D9i7V528SH0cCiSSUVYmTVDfubPmtlqtNJG1d++Gz4uIrFP//kDz5tK+gWVl8u3KyoBPPwVOnAB+85ual24g28IeKyIzzp+XeqlqU1S5uEjrVLGoIqLu3YE//Qlo1qzmtllZwNtv17xpO9kWjRC8CFRNer0eXl5eKCoqgmdNy/eS6srLpSv+0tJqd3l0y5ZSUdW6dcPnRkS24+efgWXLgOvXa26r0QBDh0obPbu4NHxuVD+1/f3NwkplLKys17FjwJo1wLVrtWvfrp20vQWv8CEic0pKpGHB3NzatW/ZEhgzBoiMrHmuFqmPhZWVYmFlfa5fl+ZSHTlS+/sMHAg895y0XQ0RkRyDQdqgvS4bM3fqJP18CQpquLyo7lhYWSkWVtajsBD4v/8Dfvyx9gv3ubhICwJyPhUR1cXBg8Bnn0nr4dWGRgPExgIjRwItWjRsblQ7LKysFAurxldUJO3ftWNH3VZCbtsWmDwZ8PNruNyIyH798gvwr39J61nVloODdLXh8OHSUCE1HhZWVoqFVeO5dEnqjs/OlramqS0HB+mvxuHDa950lYhIicEg/WG3aVPd/rDTaqWe8qFDgdDQBkuPFLCwslIsrNRVWip1we/eDZw+Xff7BwcDEyYAbdpYPDUiasLy86WhwbNn637f0FBpy6yHH+ZVhGpiYWWlWFg1PIMBOHcOyMwEcnKAu3fr/hjNmgFPPgkMGiT9pUhEZGlCALt2AevXS1cQ1pWLCxAVBfTtC0RE8GdVQ2NhZaVYWDWM8nJpH79Dh6RbcXH9HkejkbamGDVKWkGZiKih3b4NfPcdsHWr9IdhfXh4AN26SQuUduoEODtbNkdiYWW1WFhZhhDA5cvS+jAnT0rd6aWlD/aY3btLvVQc9iOixpCfD/z3v9L0hQfh5AR07CjdOnSQLrxhb9aDY2FlpVhY1c+tW9I2M+fPA3l50q0+XefmdO0qFVQhIZZ5PCKiB3H5stSDdeCAZR7P1RVo3x4IC5OKrNBQgL9+6o6FlZViYaWstFTaCqLq7coV4OZNyz5P5RU2w4axoCIi63T1qrS91v79dbuSuTa8vaUiKyAACAyUvgYE1G6Pw6aKhZWVasqFVXm5NPepuBjQ66Vi6f6bXt+wOXh4SIvuDR4s/WAhIrJ2er00yX3HDmkdvobk4QH4+kprZvn4/Hpr0ULq5WreHHB0bNgcrBULKytlq4WVwQDcuweUlf16u3sXuHNHulX9d+Xt9u1fi6ji4tqvOGxpWq00qbNfP2nYj2tREZEtqqiQ9jTdu1fagqsu62BZUrNmUgFWeWveXBpudHOTblX/Xfl/J6dfb87Otjnnq7a/v6227ly2bBn+8pe/QKfToXv37vjrX/+KPn36yLZft24d5s2bh/PnzyM8PBzvvfceRowYYYwLIbBgwQIsX74chYWF6N+/P/7+978jPDzc2KagoABTp07Fxo0bodVqMXr0aHz00UdoXuXysCNHjuDll19GdnY2WrVqhalTp2LWrFkN8yLU4Nw56UNWUSFN5q6okAqg+/9febv//+aOVS2cqt7qe6VKY9FqpUmbUVFAr17cKJmIbJ+Dg3SRTffu0h+qOTnSMOHp0+r+jL59W7rl59f/MbTaX4ssR0fpq5OTdI5arXRzcPj1/zV91Wqlq7o1GtN/d+kiTeJXk1UWVmvWrEFKSgpSU1MRHR2NDz/8EPHx8Th16hT8zOwnsmfPHowdOxaLFi3C448/jtWrVyMhIQEHDhxA165dAQCLFy/G0qVLsXLlSoSFhWHevHmIj4/HiRMn4OrqCgBISkrCzz//jPT0dJSVlWHixImYMmUKVq9eDUCqVh999FHExcUhNTUVR48exYsvvghvb29MmTJFvRfof86fBzZvVv1prVazZtIHqHt3qYfK3b2xMyIiahjNmklLwwwYIBU5x48Dhw9LXxtrdKAuDAZpTu2DXs1dEzc39QsrqxwKjI6ORu/evfHxxx8DAAwGA4KDgzF16lTMnj27WvvExESUlJRg06ZNxmN9+/ZFVFQUUlNTIYRAUFAQZsyYgZkzZwIAioqK4O/vjxUrVmDMmDHIzc1F586dkZ2djV69egEA0tLSMGLECFy+fBlBQUH4+9//jtdffx06nQ7O/1skZPbs2Vi/fj1OnjxZq3Oz5FDgtm3Al18+0EPYNCcn6UqXiAjpxkuKiaipMxik7btOnwZOnZL2JazPIsn24umngfh4yzyWzQ4F3rt3Dzk5OZgzZ47xmFarRVxcHDIzM83eJzMzEykpKSbH4uPjsX79egBAXl4edDod4uLijHEvLy9ER0cjMzMTY8aMQWZmJry9vY1FFQDExcVBq9UiKysLTz31FDIzMzFw4EBjUVX5PO+99x5++eUXtDCzBXlpaSlKq5TkegvOzm5Kc4W0WiAoSLpcODRUugUFsZAiIqpKq5WudA4JAR55RCq0rlwBLl4ELlyQbpcvN978LLVpNOo/p9UVVjdu3EBFRQX8/f1Njvv7+8v2Cul0OrPtdTqdMV55TKnN/cOMjo6O8PHxMWkTFhZW7TEqY+YKq0WLFuGNN96QP+EH0BjfMA3NyUm6IiUwUCqcKr/6+TXdK1GIiOpLq5X2PA0OBvr3l46VlwM6nflbWVnj5mtpjfHHN39VNbA5c+aY9Kbp9XoEBwdb5LFtrcfKxUWaRO7pKX318vr1st7Km4eHfRaMRETWwtFR2mHi/l0mhJCu4L55EygokG6V/668uru4uOHnRVkSe6wA+Pr6wsHBAfn3XW6Qn5+PgIAAs/cJCAhQbF/5NT8/H4GBgSZtoqKijG2uXbtm8hjl5eUoKCgweRxzz1P1Oe7n4uIClwbaflytSrzqZbL3XzJb9ZLa+y+vdXOTLsOtLKS4CzsRkfXSaKSf156e0rQLOaWl0m4YlcvpVF1mx9wyPKWlv15hfu+e1GNW+VWNc1Kb1RVWzs7O6NmzJzIyMpCQkABAmryekZGB5ORks/eJiYlBRkYGpk+fbjyWnp6OmJgYAEBYWBgCAgKQkZFhLKT0ej2ysrLw0ksvGR+jsLAQOTk56NmzJwBg69atMBgMiI6ONrZ5/fXXUVZWBicnJ+PzdOzY0ewwYEMLDQUSE00vTdVoTC8/vf9yVKX/azTViydHR/YgERHRr1xcpFvLlg/2OEKYX9qn6tJBcl+rLhVUucSQwSB9rbwZDNIFTqoTVujLL78ULi4uYsWKFeLEiRNiypQpwtvbW+h0OiGEEC+88IKYPXu2sf3u3buFo6OjeP/990Vubq5YsGCBcHJyEkePHjW2effdd4W3t7f49ttvxZEjR8SoUaNEWFiYuHPnjrHN8OHDRY8ePURWVpb48ccfRXh4uBg7dqwxXlhYKPz9/cULL7wgjh07Jr788kvRrFkz8Y9//KPW51ZUVCQAiKKiogd5iYiIiEhFtf39bZWFlRBC/PWvfxVt27YVzs7Ook+fPmLv3r3G2KBBg8T48eNN2q9du1Z06NBBODs7iy5duojvvvvOJG4wGMS8efOEv7+/cHFxEcOGDROnTp0yaXPz5k0xduxY0bx5c+Hp6SkmTpwoiouLTdocPnxYxMbGChcXF9G6dWvx7rvv1um8WFgRERHZntr+/rbKdazsma1uaUNERNSU1fb3N1cBIiIiIrIQFlZEREREFsLCioiIiMhCWFgRERERWQgLKyIiIiILYWFFREREZCEsrIiIiIgshIUVERERkYWwsCIiIiKyEKvbhNneVS50r9frGzkTIiIiqq3K39s1bVjDwkplxcXFAIDg4OBGzoSIiIjqqri4GF5eXrJx7hWoMoPBgKtXr8LDwwMajcZij6vX6xEcHIxLly7Z5R6E9n5+gP2fo72fH2D/58jzs332fo4NeX5CCBQXFyMoKAharfxMKvZYqUyr1aJNmzYN9vienp52+WGpZO/nB9j/Odr7+QH2f448P9tn7+fYUOen1FNViZPXiYiIiCyEhRURERGRhbCwshMuLi5YsGABXFxcGjuVBmHv5wfY/zna+/kB9n+OPD/bZ+/naA3nx8nrRERERBbCHisiIiIiC2FhRURERGQhLKyIiIiILISFFREREZGFsLCyUu+++y40Gg2mT59uPHb37l28/PLLaNmyJZo3b47Ro0cjPz/f5H4XL17EyJEj0axZM/j5+eGVV15BeXm5SZvt27fj4YcfhouLC9q3b48VK1aocEbVmTvHwYMHQ6PRmNx+//vfm9zPWs9x4cKF1XKPiIgwxu3h/avpHG35/at05coVPP/882jZsiXc3NwQGRmJ/fv3G+NCCMyfPx+BgYFwc3NDXFwczpw5Y/IYBQUFSEpKgqenJ7y9vTFp0iTcunXLpM2RI0cwYMAAuLq6Ijg4GIsXL7aK85swYUK193D48OE2c36hoaHV8tdoNHj55ZcB2P7nsKbzs/XPYEVFBebNm4ewsDC4ubnhoYcewltvvWWyP5/VfwYFWZ19+/aJ0NBQ0a1bNzFt2jTj8d///vciODhYZGRkiP3794u+ffuKfv36GePl5eWia9euIi4uThw8eFBs3rxZ+Pr6ijlz5hjb/PTTT6JZs2YiJSVFnDhxQvz1r38VDg4OIi0tTc1TlD3HQYMGicmTJ4uff/7ZeCsqKjLGrfkcFyxYILp06WKS+/Xr141xe3j/ajpHW37/hBCioKBAhISEiAkTJoisrCzx008/ie+//16cPXvW2Obdd98VXl5eYv369eLw4cPiySefFGFhYeLOnTvGNsOHDxfdu3cXe/fuFbt27RLt27cXY8eONcaLioqEv7+/SEpKEseOHRNffPGFcHNzE//4xz8a/fzGjx8vhg8fbvIeFhQUmDyOtZ6fEEJcu3bNJPf09HQBQGzbtk0IYfufw5rOz9Y/g++8845o2bKl2LRpk8jLyxPr1q0TzZs3Fx999JGxjbV/BllYWZni4mIRHh4u0tPTxaBBg4xFR2FhoXBychLr1q0zts3NzRUARGZmphBCiM2bNwutVit0Op2xzd///nfh6ekpSktLhRBCzJo1S3Tp0sXkORMTE0V8fHwDn9mv5M5RCFHt//ez5nNcsGCB6N69u9mYvbx/SucohG2/f0II8eqrr4rY2FjZuMFgEAEBAeIvf/mL8VhhYaFwcXERX3zxhRBCiBMnTggAIjs729jm//7v/4RGoxFXrlwRQgjxt7/9TbRo0cJ4zpXP3bFjR0ufkomazk8IqbAaNWqUbNyaz8+cadOmiYceekgYDAa7+RxWVfX8hLD9z+DIkSPFiy++aHLs6aefFklJSUII2/gMcijQyrz88ssYOXIk4uLiTI7n5OSgrKzM5HhERATatm2LzMxMAEBmZiYiIyPh7+9vbBMfHw+9Xo/jx48b29z/2PHx8cbHUIPcOVZatWoVfH190bVrV8yZMwe3b982xqz9HM+cOYOgoCC0a9cOSUlJuHjxIgD7ev/kzrGSLb9/GzZsQK9evfDss8/Cz88PPXr0wPLly43xvLw86HQ6k/y8vLwQHR1t8j56e3ujV69exjZxcXHQarXIysoythk4cCCcnZ2NbeLj43Hq1Cn88ssvjXZ+lbZv3w4/Pz907NgRL730Em7evGmMWfP53e/evXv4/PPP8eKLL0Kj0djV5xCofn6VbPkz2K9fP2RkZOD06dMAgMOHD+PHH3/EY489BsA2PoPchNmKfPnllzhw4ACys7OrxXQ6HZydneHt7W1y3N/fHzqdztim6oelMl4ZU2qj1+tx584duLm5Wep0zFI6RwD4zW9+g5CQEAQFBeHIkSN49dVXcerUKXzzzTeK+VfGlNo09DlGR0djxYoV6NixI37++We88cYbGDBgAI4dO2Y375/SOXp4eNj0+wcAP/30E/7+978jJSUFr732GrKzs/HHP/4Rzs7OGD9+vDFHc/lVzd/Pz88k7ujoCB8fH5M2YWFh1R6jMtaiRYtGOT8AGD58OJ5++mmEhYXh3LlzeO211/DYY48hMzMTDg4OVn1+91u/fj0KCwsxYcIE43Pbw+ew0v3nB9j2z1AAmD17NvR6PSIiIuDg4ICKigq88847SEpKMsnRmj+DLKysxKVLlzBt2jSkp6fD1dW1sdNpELU5xylTphj/HRkZicDAQAwbNgznzp3DQw89pFaq9VL5FxUAdOvWDdHR0QgJCcHatWtV+0Hb0JTOcdKkSTb9/gGAwWBAr1698Oc//xkA0KNHDxw7dgypqanGwsOW1eb8xowZY2wfGRmJbt264aGHHsL27dsxbNiwRsm7vv71r3/hscceQ1BQUGOn0iDMnZ+tfwbXrl2LVatWYfXq1ejSpQsOHTqE6dOnIygoyGY+gxwKtBI5OTm4du0aHn74YTg6OsLR0RE7duzA0qVL4ejoCH9/f9y7dw+FhYUm98vPz0dAQAAAICAgoNrVLZX/r6mNp6dng//yr+kcKyoqqt0nOjoaAHD27FnF/CtjSm3UOMeqvL290aFDB5w9exYBAQE2//6ZU/UczbG19y8wMBCdO3c2OdapUyfjcGdljubyq5r/tWvXTOLl5eUoKCio03vdEGo6P3PatWsHX19fk/fQWs+vqgsXLuCHH37Ab3/7W+Mxe/ocmjs/c2ztM/jKK69g9uzZGDNmDCIjI/HCCy/gT3/6ExYtWmSSozV/BllYWYlhw4bh6NGjOHTokPHWq1cvJCUlGf/t5OSEjIwM431OnTqFixcvIiYmBgAQExODo0ePmnxDpaenw9PT0/jDNCYmxuQxKttUPkZjnqODg0O1+xw6dAiA9AuhMn9rPseqbt26hXPnziEwMBA9e/a0+ffPnKrnaI6tvX/9+/fHqVOnTI6dPn0aISEhAICwsDAEBASY5KfX65GVlWXyPhYWFiInJ8fYZuvWrTAYDMZfcjExMdi5cyfKysqMbdLT09GxY8cGHSar6fzMuXz5Mm7evGnyHlrr+VX16aefws/PDyNHjjQes6fPobnzM8fWPoO3b9+GVmtamjg4OMBgMACwkc/gA09/pwZz/9Udv//970Xbtm3F1q1bxf79+0VMTIyIiYkxxisvo3300UfFoUOHRFpammjVqpXZy2hfeeUVkZubK5YtW9Yoyy1UqnqOZ8+eFW+++abYv3+/yMvLE99++61o166dGDhwoLG9NZ/jjBkzxPbt20VeXp7YvXu3iIuLE76+vuLatWtCCPt4/5TO0dbfPyGkZUAcHR3FO++8I86cOSNWrVolmjVrJj7//HNjm3fffVd4e3uLb7/9Vhw5ckSMGjXK7KXePXr0EFlZWeLHH38U4eHhJpd6FxYWCn9/f/HCCy+IY8eOiS+//FI0a9aswZcjqOn8iouLxcyZM0VmZqbIy8sTP/zwg3j44YdFeHi4uHv3rtWfX6WKigrRtm1b8eqrr1aL2cPnUO787OEzOH78eNG6dWvjcgvffPON8PX1FbNmzTK2sfbPIAsrK3Z/YXXnzh3xhz/8QbRo0UI0a9ZMPPXUU+Lnn382uc/58+fFY489Jtzc3ISvr6+YMWOGKCsrM2mzbds2ERUVJZydnUW7du3Ep59+qsLZmFf1HC9evCgGDhwofHx8hIuLi2jfvr145ZVXTNZgEcJ6zzExMVEEBgYKZ2dn0bp1a5GYmGiyPpA9vH9K52jr71+ljRs3iq5duwoXFxcREREh/vnPf5rEDQaDmDdvnvD39xcuLi5i2LBh4tSpUyZtbt68KcaOHSuaN28uPD09xcSJE0VxcbFJm8OHD4vY2Fjh4uIiWrduLd59990GPzchlM/v9u3b4tFHHxWtWrUSTk5OIiQkREyePNnk0nxrPz8hhPj+++8FgGrvixD28TmUOz97+Azq9Xoxbdo00bZtW+Hq6iratWsnXn/9dZNlEaz9M6gRospypkRERERUb5xjRURERGQhLKyIiIiILISFFREREZGFsLAiIiIishAWVkREREQWwsKKiIiIyEJYWBERERFZCAsrIrJbGo0GgwcPfqDH2L59OzQaDRYuXGiRnJRYIl8558+fh0ajwYQJExrk8YlIwsKKiBrM3r17odFoMHz4cLPx6dOnQ6PRICIiwmz8ww8/hEajwbx58xoyTYtryAKJiKybY2MnQET2q1evXmjevDl2796N8vJyODqa/sjZtm0bNBoNTp06BZ1OV21X+W3btgEAhg4dWq/nz83NRbNmzeqXfCOwtXyJqDr2WBFRg3F0dMSAAQNw69YtZGdnm8Ru3ryJo0eP4qmnngLwaxFVyWAwYNeuXXBxcTHuWl9XERERaNu2bf2SbwS2li8RVcfCioga1JAhQwBIc5Wq2rFjB4QQ+OMf/wgfH59qhdXhw4fxyy+/ICYmBq6ursbjR44cwZgxYxAYGAhnZ2eEhIRg6tSpuHnzZrXnlhuSO3/+PBITE+Hj44PmzZtj0KBB2LlzJxYuXAiNRlMt10r79+/HI488Ag8PD3h5eeGpp57C+fPnjfHK+ViV56fRaIy3FStW1Phamct3woQJ0Gg0yMvLw9KlSxEREQEXFxeEhITgjTfegMFgqPFxldy7dw/PPfccNBoNZs2aharbx+7YsQMDBw6Eu7s7WrZsicTERFy6dAmDBw82nicRmeJQIBE1qMrCatu2bZgzZ47x+LZt2+Dm5oa+fftiwIAB1Qqryv9X3h8ANmzYgOeeew5arRajRo1CcHAwTpw4gY8//hjff/89srKy0KJFC8V8rly5gn79+uHnn3/G8OHD0aNHD5w6dQqPPPKI4pBjdnY2Fi9ejCFDhuB3v/sdDh48iPXr1+Po0aM4duwYXF1dERoaigULFuCNN95ASEiIyUTxqKio2r5kZr3yyivYsWMHHn/8ccTHx2P9+vVYuHAh7t27h3feeadej1lcXIyEhARs27YNS5YsQUpKijG2ZcsWjBw5Eg4ODkhMTERQUBC2bduG2NjYGl9joiZNEBE1oPLycuHl5SXc3d3FvXv3jMe7du0qhgwZIoQQ4oMPPhAAxKVLl4zxJ554QgAQO3fuFEIIcePGDeHp6Slat24tzp8/b/IcX3zxhQAgkpOTTY4DEIMGDTI59vzzzwsA4p133jE5/q9//UsAEADEtm3bjMe3bdtmPP7ll1+a3OeFF14QAMQXX3xR4/PWhrn7jR8/XgAQYWFh4urVq8bj169fF97e3sLDw0OUlpbW+Nh5eXkCgBg/frwQQgidTid69OghnJycxH/+8x+TtuXl5SIkJERoNBqxa9cuk9i4ceOMrwcRVcehQCJqUA4ODhg4cCBKSkqwb98+AMD169dx/Phx47DXoEGDAPzaS1U5v8rNzQ3R0dEAgM8++wx6vR6LFi1CSEiIyXOMGTMGDz/8ML788kvFXEpLS7Fu3Tr4+flhxowZJrGJEyeiY8eOsvcdOHAgEhMTTY69+OKLAFBt/lhDmDdvHgIDA43/9/X1xahRo1BcXIxTp07V6bHOnTuH/v3749SpU9iwYQOef/55k/iPP/6ICxcu4IknnkBsbKxJ7O2334aDg0P9T4TIznEokIga3ODBg7Fx40Zs27YN/fv3x/bt2yGEMBZWUVFR8PLywrZt2/DCCy/g0KFDKCwsRFxcHJydnQFISzcAQFZWFs6dO1ftOe7evYsbN27gxo0b8PX1NZvHqVOnUFpail69esHFxcUkptFo0K9fP9kipWfPntWOtWnTBgBQWFhYq9fhQVjq+U+ePIn+/fujvLwcW7duNRauVR0+fBgAqhVVABAcHIy2bdsiLy+v1s9J1JSwsCKiBld1AvvcuXOxfft2uLq6Gn+pa7VaxMbGGnuszC2zUFBQAABYtmyZ4nOVlJTIFlZ6vR4A4OfnZzbu7+8v+7ienp7VjlUuH1FRUaGYkyVY6vlPnz6NX375Bf369UPXrl3NtqnN68TCisg8DgUSUYPr3r07WrRogT179uDevXvYtm0b+vbta9JrNHjwYJw/fx7nz583XpVXdeJ6ZWFx9OhRCCFkb/cPE1ZV+RjXrl0zG8/Pz3/QU7V6Tz75JBYuXIg9e/ZgxIgRKCkpqdaGrxNR/bGwIqIGp9VqMWjQINy5cwcbNmxAbm5utWUFKudZ/fDDD9i1axeaN2+OXr16GeOVvVuZmZn1zqNjx45wcXFBTk4OSktLTWJCiAd67Kq0Wq0qvVj1tWDBArz11lvYuXMnHnvsMdy6dcsk3r17dwDA7t27q9338uXLuHjxoip5EtkiFlZEpIrK3qc33ngDAKoVVg8//DA8PDzw0UcfoaioCAMGDDBZqX3ixInw8PDA66+/juPHj1d7/Nu3bxvnYclxcXHBM888g/z8fHz44Ycmsc8++wwnT56sx5lV5+Pjg8uXL1vksRrK3Llz8c4772DXrl3ViqvY2Fi0bdsWGzdurFZszps3z6qLRqLGxjlWRKSKysKqcs2nvn37msQdHBzQv39/pKWlmbSv1KpVK3zxxRd49tln0b17dwwfPhwREREoLS3F+fPnsWPHDvTr1894fzmLFi3CDz/8gNmzZ2PHjh3Gdaw2bdqE4cOHIy0tDVrtg/3NOXToUKxduxYJCQno0aMHHBwc8OSTT6Jbt24P9LiW9tprr0Gr1WLOnDnGc2/evDkcHByQmpqKJ598EkOHDkViYiICAwOxY8cOXLlyBd27d8eRI0caO30iq8TCiohU0bVrV/j6+uLGjRvV5ldVGjRokGxhBQAjR47EwYMH8Ze//AU//PAD0tPT4e7ujjZt2mDixInVlg0wJzg4GJmZmXj11VexZcsW7NixAz179sSWLVuwbt06AOYnitfFRx99BADYunUrNm7cCIPBgDZt2lhdYQUAs2fPhlarxauvvor4+HikpaXBw8MDjz32GLZs2YL58+dj7dq1cHNzw7Bhw7BmzRqMGDHigV8jInulEaLK/gVERE1YbGwsMjMzUVRUhObNmzd2OlapuLgY/v7+iIyMRFZWVmOnQ2R1OMeKiJqcn3/+udqxzz//HLt370ZcXByLKkjLVhQXF5scq6iowCuvvII7d+4gISGhcRIjsnLssSKiJqdly5bo0aMHOnfuDAcHBxw6dAjbt2+Hh4cHdu/ejcjIyMZOsdEdOnQIsbGxiI+PR7t27VBcXIxdu3bhxIkT6NKlC7KysuDu7t7YaRJZHRZWRNTkvP7669i4cSMuXryIkpIStGrVCkOGDMG8efMQERHR2OlZhevXr2PWrFnYsWMH8vPzUV5ejrZt2yIhIQGvv/46vL29GztFIqvEwoqIiIjIQjjHioiIiMhCWFgRERERWQgLKyIiIiILYWFFREREZCEsrIiIiIgshIUVERERkYWwsCIiIiKyEBZWRERERBbCwoqIiIjIQv4/LnP0SBXi800AAAAASUVORK5CYII=\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Plot the prior distribution\n",
        "plt.figure()\n",
        "x = np.linspace(6000 - 4*500, 6000 + 4*500, 1000)  # mean = 6000, std = 500, hence the range is mean ± 4*std\n",
        "plt.plot(x, norm.pdf(x, 6000, 500),'b-', lw = 5, alpha = 0.6)  # mean = 6000, std = 500 for the prior\n",
        "plt.title('Prior Distribution', size=14)\n",
        "plt.xlabel('Weight in kg', size=14)\n",
        "plt.ylabel('PDF', size=14)\n",
        "\n",
        "# Normal prior\n",
        "p_dist = pd.DataFrame(index=np.linspace(6000 - 4*500, 6000 + 4*500, 1000))  # Use the same range as for the x-axis\n",
        "p_dist['probs'] = [norm.pdf(x, 6000, 500) for x in p_dist.index]  # Use the same mean and std\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a9143599-2fb6-4bf8-8e73-1a40861b3a4f",
      "metadata": {
        "id": "a9143599-2fb6-4bf8-8e73-1a40861b3a4f"
      },
      "source": [
        "# Joint Priors - 10 Points"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "id": "50b63781-c299-4050-a5a4-16adc5f1e70f",
      "metadata": {
        "id": "50b63781-c299-4050-a5a4-16adc5f1e70f"
      },
      "outputs": [],
      "source": [
        "# Multiplies probabilities from two distributions\n",
        "\n",
        "def make_joint(pmf1, pmf2):\n",
        "    \"\"\"\n",
        "    Compute the outer product of two PMFs to create a joint distribution.\n",
        "\n",
        "    Parameters:\n",
        "    pmf1: DataFrame representing the first PMF with probabilities.\n",
        "    pmf2: DataFrame representing the second PMF with probabilities.\n",
        "\n",
        "    Returns:\n",
        "    A DataFrame representing the joint distribution of the two PMFs.\n",
        "    \"\"\"\n",
        "    # Create a meshgrid which will represent all possible pairs of probabilities from pmf1 and pmf2\n",
        "    X, Y = np.meshgrid(pmf1['probs'], pmf2['probs'])\n",
        "\n",
        "    # Compute the outer product to get the joint probabilities\n",
        "    # The resulting matrix will have probabilities where rows correspond to values from pmf1 and columns to values from pmf2\n",
        "    joint_pmf = pd.DataFrame(X * Y, columns=pmf1.index, index=pmf2.index)\n",
        "\n",
        "    return joint_pmf\n",
        "\n",
        "# Usage example with blanks filled in:\n",
        "# joint_distribution = make_joint(pmf1, pmf2)\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Define a normal distribution for the prior with mean and standard deviation\n",
        "# Replace '____' with appropriate values for mean and standard deviation\n",
        "\n",
        "# mean_weight = 6000  # The provided mean weight of an adult African elephant\n",
        "# std_dev_weight = 500  # The provided standard deviation of the weight\n",
        "\n",
        "p_dist = pd.DataFrame(index=np.linspace(3000, 9000, 161))\n",
        "p_dist['probs'] = [norm.pdf(x, 6000, 500) for x in p_dist.index]\n",
        "\n",
        "p_dist['probs'] = p_dist['probs'] / sum(p_dist['probs'])\n",
        "\n",
        "# Assuming make_joint is defined as in the previous steps\n",
        "joint = make_joint(p_dist, p_dist)\n",
        "\n",
        "# Plotting the joint prior distribution\n",
        "plt.figure()\n",
        "plt.pcolormesh(joint.columns, joint.index, joint, cmap='Blues')\n",
        "plt.colorbar()\n",
        "plt.xlabel('Weight of A in kg', size=14)\n",
        "plt.ylabel('Weight of B in kg', size=14)\n",
        "plt.title('Joint prior distribution of weight for A and B', size=14)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 496
        },
        "id": "gmgjnun8klVF",
        "outputId": "ddda8edc-bace-44a3-ab68-e8455c2ed953"
      },
      "id": "gmgjnun8klVF",
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Joint prior distribution of weight for A and B')"
            ]
          },
          "metadata": {},
          "execution_count": 4
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "84c8a60f-3257-48d2-a9e8-9fbd0086959b",
      "metadata": {
        "id": "84c8a60f-3257-48d2-a9e8-9fbd0086959b"
      },
      "source": [
        "Joint Likelihood\n",
        "\n",
        "Now that we have a joint prior distribution, we can update it with the data, which is that elephant A is heavier than B."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "id": "efced181-954e-4a9e-aeed-4c87fa74d0b9",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "id": "efced181-954e-4a9e-aeed-4c87fa74d0b9",
        "outputId": "30abb654-33f0-43ea-afea-755c2616daf8"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Likelihood of A being heavier than B')"
            ]
          },
          "metadata": {},
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# create a grid of weights for A and B\n",
        "A, B = np.meshgrid(joint.index, joint.columns)  # Q1: Fill in the attribute for elephant A's weight range, Q2: Fill in the attribute for elephant B's weight range.\n",
        "\n",
        "# Check if A is heavier than B (and add 0 to make it numeric)\n",
        "A_heavier = (A > B) + 0  # Q3: Fill in the comparison operator to check if A's weight is greater than B's weight.\n",
        "\n",
        "# Create a DataFrame with the likelihood of A being heavier than B\n",
        "likelihood = pd.DataFrame(A_heavier, index=joint.index, columns=joint.columns)  # Q4 & Q5: Fill in the attributes for the index and columns from `joint`.\n",
        "\n",
        "plt.figure()\n",
        "plt.pcolormesh(likelihood.columns, likelihood.index, likelihood, cmap='Blues')  # Q6: Use `likelihood.columns` and `likelihood.index`, Q7: Fill in the colormap name.\n",
        "plt.colorbar()\n",
        "plt.xlabel('Weight of A in kg', size=14)  # Q8: Fill in the label for x-axis and the text size.\n",
        "plt.ylabel('Weight of B in kg', size=14)  # Q9: Fill in the label for y-axis and the text size.\n",
        "plt.title('Likelihood of A being heavier than B', size=16)  # Q10: Fill in the title of the plot and the text size.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "fda05643-2e3d-42e9-99aa-7635014d3960",
      "metadata": {
        "id": "fda05643-2e3d-42e9-99aa-7635014d3960"
      },
      "source": [
        "# The Update - 10 Points\n",
        "\n",
        "Update the posterior, which is the joint prior times the joint likelihood."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "id": "a493dae9-a201-4c02-aaa7-88b980e34f8c",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 497
        },
        "id": "a493dae9-a201-4c02-aaa7-88b980e34f8c",
        "outputId": "78c7a604-8f26-4d89-e7ff-5bff8ca92ba9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Joint posterior distribution of weight for A and B')"
            ]
          },
          "metadata": {},
          "execution_count": 6
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 2 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Update the posterior by multiplying the joint prior with the likelihood\n",
        "posterior = joint * likelihood\n",
        "\n",
        "# Calculate the probability of the data by summing all the probabilities in the posterior\n",
        "prob_data = posterior.values.sum()  # <-- Fill in the method to convert the DataFrame to a numpy array\n",
        "\n",
        "# Normalize the posterior by dividing by the probability of the data\n",
        "posterior = posterior / prob_data\n",
        "\n",
        "# Plotting the joint posterior distribution\n",
        "plt.figure()\n",
        "plt.pcolormesh(posterior.columns, posterior.index, posterior, cmap='Blues')  # Q1: Fill in posterior column attribute, Q2: Fill in posterior index attribute, Q3: Fill in the colormap name\n",
        "plt.colorbar()\n",
        "plt.xlabel('Weight of A in kg', size=14)  # Q4: Fill in the text size\n",
        "plt.ylabel('Weight of B in kg', size=14)  # Q5: Fill in the text size\n",
        "plt.title('Joint posterior distribution of weight for A and B', size=16)  # Q6: Fill in the text size\n",
        "\n",
        "# Remember to replace the blanks with the correct code based on the comments provided.\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "9912eb11-4aa1-467c-a82b-b72d6b6bf576",
      "metadata": {
        "id": "9912eb11-4aa1-467c-a82b-b72d6b6bf576"
      },
      "source": [
        "# Marginal Distribution\n",
        "\n",
        "Compute the posterior distribution of weights for elephant A."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "id": "c734f578-56ca-437f-906c-f8885f998152",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 496
        },
        "id": "c734f578-56ca-437f-906c-f8885f998152",
        "outputId": "136d7830-cd6f-4688-ff43-ce8af4fe1ca9"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'PDF')"
            ]
          },
          "metadata": {},
          "execution_count": 7
        },
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Sum over the rows of the joint posterior to get the marginal for A\n",
        "marginal_A = posterior.sum(axis=0)\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "p_dist.plot(ax=ax, style='--')\n",
        "marginal_A.plot(ax=ax)\n",
        "ax.legend(['Prior', 'Posterior for A'], fontsize=14, loc='best')\n",
        "plt.title('Prior and Posterior Distribution', size=14)\n",
        "plt.xlabel('Weight in kg', size=14)\n",
        "plt.ylabel('PDF', size=14)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "id": "ad70d997-e731-4d01-b5f7-43757da2c7ac",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ad70d997-e731-4d01-b5f7-43757da2c7ac",
        "outputId": "9d82a447-91fa-416d-d690-26c235510d6f"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "6288.1245451090745"
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ],
      "source": [
        "# Calculate the MMSE weight for A.\n",
        "mmse_weight_A = sum(marginal_A.index * marginal_A)\n",
        "\n",
        "mmse_weight_A"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "51d51229-bcd6-4ac8-998e-2af4d4e840ab",
      "metadata": {
        "id": "51d51229-bcd6-4ac8-998e-2af4d4e840ab"
      },
      "source": [
        "# Elephant B Computation - 10 Points\n",
        "\n",
        "#### Following the example for the posterior distribution of weights for elephant A, now calculate and plot the posterior distribution of weights for elephant B and calculate it's MMSE"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 9,
      "id": "3776a075-dc14-42fc-9e85-07d288a87fe6",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 496
        },
        "id": "3776a075-dc14-42fc-9e85-07d288a87fe6",
        "outputId": "521d873a-3428-4572-cbf0-6e5f917b1ffd"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "5711.875454890925"
            ]
          },
          "metadata": {},
          "execution_count": 9
        }
      ],
      "source": [
        "# Write your code here\n",
        "\n",
        "# Sum over the columns of the joint posterior to get the marginal for B\n",
        "marginal_B = posterior.sum(axis=1)\n",
        "\n",
        "# Plot the Marginal Distribution for B\n",
        "\n",
        "fig, ax = plt.subplots()\n",
        "p_dist.plot(ax=ax, style='--')  # Assuming p_dist is the prior distribution as mentioned in previous snippets\n",
        "marginal_B.plot(ax=ax)\n",
        "ax.legend(['Prior', 'Posterior for B'], fontsize=14, loc='best')\n",
        "plt.title('Prior and Posterior Distribution for B', size=14)\n",
        "plt.xlabel('Weight in kg', size=14)\n",
        "plt.ylabel('PDF', size=14)\n",
        "plt.show()\n",
        "\n",
        "# Calculate the MMSE weight for B\n",
        "mmse_weight_B = sum(marginal_B.index * marginal_B)\n",
        "\n",
        "mmse_weight_B\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "2a03267d-aad3-412c-8f48-e57c5444317f",
      "metadata": {
        "id": "2a03267d-aad3-412c-8f48-e57c5444317f"
      },
      "source": [
        "# Conditional Posteriors - 5 Points (Bonus)\n",
        "\n",
        "Suppose we now measure A and find that it weighs 6500 kg. What does that tell us about the weight of B?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 10,
      "id": "2b551c85-6047-4848-bdd2-eb9c909eb6ec",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 478
        },
        "id": "2b551c85-6047-4848-bdd2-eb9c909eb6ec",
        "outputId": "156b939c-a83e-44d4-c541-f05f6b242cde"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 640x480 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {}
        }
      ],
      "source": [
        "# Find the column index closest to the given weight\n",
        "\n",
        "# Q1: Replace 6500 with the desired weight to find the closest column.\n",
        "closest_weight = min(posterior.columns, key=lambda x: abs(x-6500))  # <-- Fill in the desired weight\n",
        "\n",
        "# Extract the column for the closest weight\n",
        "\n",
        "# Q2: Replace 'closest_weight' with the variable holding the closest weight.\n",
        "column_closest_weight = posterior[closest_weight]  # <-- Fill in the variable holding the closest weight\n",
        "# Normalize the extracted column to get a valid probability distribution\n",
        "column_closest_weight = column_closest_weight / sum(column_closest_weight)\n",
        "\n",
        "# Prepare a figure and axis for plotting with subplots\n",
        "fig, ax = plt.subplots()\n",
        "\n",
        "# Plot the prior distribution on the axis created\n",
        "# Q3: Replace 'p_dist' with the prior distribution DataFrame.\n",
        "p_dist.plot(ax=ax, style='--')  # <-- Fill in the DataFrame containing the prior distribution\n",
        "\n",
        "# Plot the conditional posterior distribution on the same axis\n",
        "# Q4: Replace 'column_closest_weight' with the normalized posterior column.\n",
        "column_closest_weight.plot(ax=ax)  # <-- Fill in the normalized posterior column\n",
        "\n",
        "# Set the legend for the plot with font size 14 and the best location\n",
        "ax.legend(['Prior', 'Conditional Posterior for B'], fontsize=14, loc='best')\n",
        "# Set the title for the plot\n",
        "# Q5: Replace 'size=14' with the desired title font size.\n",
        "plt.title('Prior and Posterior Distribution for Weight Closest to 6500 kg', size=14)  # <-- Fill in the title font size\n",
        "# Set the x-label with the desired font size\n",
        "# Q6: Replace 'size=14' with the desired label font size.\n",
        "plt.xlabel('Weight in kg', size=14)  # <-- Fill in the label font size\n",
        "# Set the y-label with the desired font size\n",
        "# Q7: Replace 'size=14' with the desired label font size.\n",
        "plt.ylabel('PDF', size=14)  # <-- Fill in the label font size\n",
        "# Display the plot\n",
        "plt.show()\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "c3119cb5-e41c-495f-aa29-5e309b43620d",
      "metadata": {
        "id": "c3119cb5-e41c-495f-aa29-5e309b43620d"
      },
      "source": [
        "# Classifying Birds - 30 Points (Bonus: 5 Points)\n",
        "\n",
        "Using a dataset of measurements of three types of birds, we’ll learn to classify a penguin as one one of those three types: Robin, Eagle and Sparrow.\n",
        "\n",
        "We’ll consider a dataset with three measurements:\n",
        "\n",
        "- Wing Length\n",
        "\n",
        "- Beak Length\n",
        "\n",
        "- Body Mass\n",
        "\n",
        "And we’ll begin to approach the problem in our typical way:\n",
        "\n",
        "Define a prior distribution for how likely we think our unknown example is to belong to each of the three possible species\n",
        "\n",
        "- Compute the likelihood of the data for each species\n",
        "\n",
        "- Compute the posterior probability of each hypothesis"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "459c63d4-127a-4900-958f-c28fa6f07f8b",
      "metadata": {
        "id": "459c63d4-127a-4900-958f-c28fa6f07f8b"
      },
      "source": [
        "Start by importing the necessary libraries. We will need `pandas` for data manipulation, `numpy` for numerical operations, and `scipy.stats` for statistical functions."
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 11,
      "id": "6a8a6b0f-8ef1-4bef-9d07-8819da4fe5c2",
      "metadata": {
        "id": "6a8a6b0f-8ef1-4bef-9d07-8819da4fe5c2"
      },
      "outputs": [],
      "source": [
        "from scipy.stats import multivariate_normal\n",
        "\n",
        "# Add any additional libraries you think you'll need below this line.\n",
        "import pandas as pd\n",
        "import numpy as np"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "397d43d5-2568-4db8-b06c-d1a5a0b58cc7",
      "metadata": {
        "id": "397d43d5-2568-4db8-b06c-d1a5a0b58cc7"
      },
      "source": [
        "# Defining the Priors - 5 Points"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "8a68b4da-1a84-486c-8d2b-4be1895cf4b3",
      "metadata": {
        "id": "8a68b4da-1a84-486c-8d2b-4be1895cf4b3"
      },
      "source": [
        "Load the dataset from a CSV file into a Pandas DataFrame. Replace the `file_path` with the actual path to your CSV file."
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "from google.colab import files\n",
        "\n",
        "def upload_files():\n",
        "    uploaded = files.upload()\n",
        "    for sdc in uploaded.keys():\n",
        "        print('Uploaded file \"{name}\" with length {length} bytes'.format(name=sdc, length=len(uploaded[sdc])))\n",
        "    return sdc  # returning the file name\n",
        "\n",
        "# Calling the function to upload files\n",
        "uploaded_file_name = upload_files()"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 95
        },
        "id": "sPePUBSNrgZW",
        "outputId": "6a5695be-8a6b-4763-876f-33788a048e90"
      },
      "id": "sPePUBSNrgZW",
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<IPython.core.display.HTML object>"
            ],
            "text/html": [
              "\n",
              "     <input type=\"file\" id=\"files-62ea2b7c-a29e-44a5-b27c-d3a15b962f03\" name=\"files[]\" multiple disabled\n",
              "        style=\"border:none\" />\n",
              "     <output id=\"result-62ea2b7c-a29e-44a5-b27c-d3a15b962f03\">\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 birds_dataset.csv to birds_dataset.csv\n",
            "Uploaded file \"birds_dataset.csv\" with length 37339 bytes\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 13,
      "id": "167854ad-873e-4c7e-a51f-e96a85a20c5b",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 206
        },
        "id": "167854ad-873e-4c7e-a51f-e96a85a20c5b",
        "outputId": "ac82b170-0eae-4b83-b75d-09e29a76c35b"
      },
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "   wing_length  beak_length  body_mass  species\n",
              "0   179.919021    22.297573  46.901258    Robin\n",
              "1   218.835690    28.937718  99.936140    Eagle\n",
              "2   155.907941    10.710851  36.686616  Sparrow\n",
              "3   161.175754    14.245663  24.597168  Sparrow\n",
              "4   161.904417    20.438017  51.000078    Robin"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-ca0cfa75-80dd-4919-9d86-b7c8dce64f02\" 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>wing_length</th>\n",
              "      <th>beak_length</th>\n",
              "      <th>body_mass</th>\n",
              "      <th>species</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>179.919021</td>\n",
              "      <td>22.297573</td>\n",
              "      <td>46.901258</td>\n",
              "      <td>Robin</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>218.835690</td>\n",
              "      <td>28.937718</td>\n",
              "      <td>99.936140</td>\n",
              "      <td>Eagle</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>155.907941</td>\n",
              "      <td>10.710851</td>\n",
              "      <td>36.686616</td>\n",
              "      <td>Sparrow</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>3</th>\n",
              "      <td>161.175754</td>\n",
              "      <td>14.245663</td>\n",
              "      <td>24.597168</td>\n",
              "      <td>Sparrow</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>4</th>\n",
              "      <td>161.904417</td>\n",
              "      <td>20.438017</td>\n",
              "      <td>51.000078</td>\n",
              "      <td>Robin</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-ca0cfa75-80dd-4919-9d86-b7c8dce64f02')\"\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",
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              "  </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-ca0cfa75-80dd-4919-9d86-b7c8dce64f02 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-ca0cfa75-80dd-4919-9d86-b7c8dce64f02');\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",
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              "        docLink.innerHTML = docLinkHtml;\n",
              "        element.appendChild(docLink);\n",
              "      }\n",
              "    </script>\n",
              "  </div>\n",
              "\n",
              "\n",
              "<div id=\"df-358a01f2-4296-4ebf-a81a-b8e3f990551d\">\n",
              "  <button class=\"colab-df-quickchart\" onclick=\"quickchart('df-358a01f2-4296-4ebf-a81a-b8e3f990551d')\"\n",
              "            title=\"Suggest charts.\"\n",
              "            style=\"display:none;\">\n",
              "\n",
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              "  </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-358a01f2-4296-4ebf-a81a-b8e3f990551d 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": [
        "# Load the dataset\n",
        "df = pd.read_csv('birds_dataset.csv')  # <-- Fill in the blank with the file path\n",
        "\n",
        "# Take a quick look at the data\n",
        "df.head()"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(df.columns)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "dBggkxkk1B4p",
        "outputId": "6424ae38-4d7f-4e9c-877f-9db8cdc149f1"
      },
      "id": "dBggkxkk1B4p",
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Index(['wing_length', 'beak_length', 'body_mass', 'species'], dtype='object')\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "f0fd628b-80bc-41d9-bff6-993724b5c6af",
      "metadata": {
        "id": "f0fd628b-80bc-41d9-bff6-993724b5c6af"
      },
      "source": [
        "Define a prior distribution for the likelihood that an example belongs to each species in the dataset. The prior should be uniform across all species if you have no prior knowledge about the likelihood of each species.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 15,
      "id": "3f6ff675-70a8-4d85-8e4d-46d4abba5466",
      "metadata": {
        "id": "3f6ff675-70a8-4d85-8e4d-46d4abba5466"
      },
      "outputs": [],
      "source": [
        "# Define a uniform prior for the species\n",
        "# In the blank after 'species', fill in the column name that contains species information\n",
        "species = np.sort(df['species'].unique()) # <-- Replace with the column name from your DataFrame that contains species names to get only unique values.\n",
        "\n",
        "# In the DataFrame constructor, fill in the variable that holds the sorted species names\n",
        "p_dist = pd.DataFrame(species, columns=['species']) # <-- Replace with the variable you defined above.\n",
        "\n",
        "# For the prior probabilities column, fill in the name of the column you want to create for storing probabilities\n",
        "p_dist['prior_probability'] = 1 / len(species) # <-- Replace with the name of the new column (probabilities column)."
      ]
    },
    {
      "cell_type": "markdown",
      "id": "5af607d7-9e69-4e47-8753-3907c031ab30",
      "metadata": {
        "id": "5af607d7-9e69-4e47-8753-3907c031ab30"
      },
      "source": [
        "# Computing Likelihood - 10 Points"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "d402c085-d148-4ef6-8dee-217dda170ab1",
      "metadata": {
        "id": "d402c085-d148-4ef6-8dee-217dda170ab1"
      },
      "source": [
        "Compute the likelihood of the observed data for each species based on the provided features. Replace `feature_names` with the actual names of the features you are using from your dataset.\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 16,
      "id": "a56f970c-3bcf-472d-82a3-a003dacafdda",
      "metadata": {
        "id": "a56f970c-3bcf-472d-82a3-a003dacafdda"
      },
      "outputs": [],
      "source": [
        "# Define a function to compute likelihoods\n",
        "def compute_likelihoods(df, feature_names):\n",
        "    # Initialize a dictionary to hold the likelihoods\n",
        "    likelihoods = {}\n",
        "    # Loop through each species and calculate its likelihood\n",
        "    for species in df['species'].unique():  # <-- 'species' is the column name that contains species information.\n",
        "        # Subset the dataframe for the current species\n",
        "        subset = df[df['species'] == species]  # <-- 'species' is the column name that contains species information.\n",
        "        # Calculate the mean and covariance of the features for this species\n",
        "        mean = subset[feature_names].mean()  # <-- Using the 'feature_names' variable.\n",
        "        cov = subset[feature_names].cov()  # <-- Using the 'feature_names' variable.\n",
        "        # Create a multivariate normal distribution\n",
        "        rv = multivariate_normal(mean, cov)  # <-- Using 'mean' and 'cov' respectively.\n",
        "        # Store the distribution in the likelihoods dictionary\n",
        "        likelihoods[species] = rv\n",
        "    return likelihoods\n",
        "\n",
        "# Use the function to compute likelihoods\n",
        "# Fill in the feature names you're using to calculate the likelihoods\n",
        "feature_names = ['wing_length', 'beak_length', 'body_mass']  # <-- Filling in the actual feature names: 'Wing Length', 'Beak Length', and 'Body Mass'.\n",
        "likelihoods = compute_likelihoods(df, feature_names)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "a5518d95-2a1f-473a-9134-4c2bbbf5cf45",
      "metadata": {
        "id": "a5518d95-2a1f-473a-9134-4c2bbbf5cf45"
      },
      "source": [
        "# Updating Posterior Probabilities - 10 Points"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "3ef1ec6f-ea44-4c55-831a-dece6ea30eb4",
      "metadata": {
        "id": "3ef1ec6f-ea44-4c55-831a-dece6ea30eb4"
      },
      "source": [
        "Once we have our likelihoods and prior, we can update the posterior probabilities. This involves multiplying the prior probabilities by the likelihoods and normalizing.\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "print(p_dist.columns)"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "sZoUdaH71naX",
        "outputId": "af9f96be-4513-48ee-cb64-48b9116dcd85"
      },
      "id": "sZoUdaH71naX",
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Index(['species', 'prior_probability'], dtype='object')\n"
          ]
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 18,
      "id": "de5181aa-55cc-4185-9e39-5e660e9c39ee",
      "metadata": {
        "id": "de5181aa-55cc-4185-9e39-5e660e9c39ee"
      },
      "outputs": [],
      "source": [
        "# Define the update function\n",
        "def update(p_dist, likelihoods, observed_data):\n",
        "    # Multiply the prior by the likelihoods\n",
        "    p_dist['prior_probability'] *= [likelihoods[species].pdf(observed_data) for species in p_dist['species']]  # Filled in the column name for species.\n",
        "    # Normalize the probabilities\n",
        "    p_dist['prior_probability'] /= p_dist['prior_probability'].sum()  # Filled in the method to sum the probabilities.\n",
        "    return p_dist\n",
        "\n",
        "# Apply the update\n",
        "# Using the observed data point\n",
        "observed_data = [160, 18, 35]  # Inputted observed feature values.\n",
        "posterior = update(p_dist, likelihoods, observed_data)\n"
      ]
    },
    {
      "cell_type": "markdown",
      "id": "4111528b-bed2-49ea-aa3d-4459f63c9464",
      "metadata": {
        "id": "4111528b-bed2-49ea-aa3d-4459f63c9464"
      },
      "source": [
        "Display the updated posterior probabilities to see the most likely species given the observed data.\n"
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Sort and display the posterior probabilities in descending order\n",
        "sorted_posterior = posterior.sort_values(by='prior_probability', ascending=False)\n",
        "print(sorted_posterior)\n"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "oWGEWWn11-H8",
        "outputId": "1f7f9764-3c52-42dc-9b29-516cc24e56d1"
      },
      "id": "oWGEWWn11-H8",
      "execution_count": 19,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   species  prior_probability\n",
            "2  Sparrow       9.803122e-01\n",
            "1    Robin       1.968779e-02\n",
            "0    Eagle       1.975966e-13\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "id": "64bf9a99-0933-441d-bced-d79f6d80453f",
      "metadata": {
        "id": "64bf9a99-0933-441d-bced-d79f6d80453f"
      },
      "source": [
        "# Printing Probabilities and Reasoning - 10 Points (Reasoning - 5 Points bonus)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 20,
      "id": "7e459cd8-efbd-44cb-9d60-77a1c163d266",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "7e459cd8-efbd-44cb-9d60-77a1c163d266",
        "outputId": "5e4ab46c-eba2-4352-fa32-959b36a7c761"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "   species  prior_probability\n",
            "2  Sparrow       9.803122e-01\n",
            "1    Robin       1.968779e-02\n",
            "0    Eagle       1.975966e-13\n"
          ]
        }
      ],
      "source": [
        "# Display the posterior probabilities\n",
        "print(sorted_posterior)\n"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "id": "eab4ac49-aa05-4291-857d-cb18689d3f3b",
      "metadata": {
        "id": "eab4ac49-aa05-4291-857d-cb18689d3f3b"
      },
      "outputs": [],
      "source": [
        "# Write your reflection below and what was the final prediction. Explain in words how using 2 features rather than 3 could have changed the outcome"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "The features, in this case, are the measurable characteristics of the birds - wing length, beak length, and body mass. If we are only using two out of the three features, we might exclude a significant distinguishing characteristic, which could lead to a less accurate prediction.\n",
        "\n",
        "For instance, imagine if 'body mass' was the most distinguishing factor between the species, but we decided to only use 'wing length' and 'beak length'. This could lead to a misclassification or a less confident prediction."
      ],
      "metadata": {
        "id": "DsAWRTNT18XV"
      },
      "id": "DsAWRTNT18XV"
    }
  ],
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    "kernelspec": {
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    "accelerator": "GPU"
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