{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# 02 Valid discrete probability distribution examples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<iframe width=\"700\" height=\"400\" src=\"https://www.youtube.com/embed/uXtxKxYl1Iw/\" frameborder=\"0\" allowfullscreen></iframe>\n"
      ],
      "text/plain": [
       "<IPython.core.display.HTML object>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%html\n",
    "<iframe width=\"700\" height=\"400\" src=\"https://www.youtube.com/embed/uXtxKxYl1Iw/\" frameborder=\"0\" allowfullscreen></iframe>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "from pandas import Series, DataFrame\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "[khanacademy](https://www.khanacademy.org/math/ap-statistics/random-variables-ap/discrete-random-variables/v/valid-discrete-probability-distribution-examples?modal=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Valid discrete probability distribution examples fig 1](./imgs/09-02-01.png)![Valid discrete probability distribution examples fig 2](./imgs/09-02-02.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "basketball_df = DataFrame({'Outcome': ['Miss both free throws', 'Make exactly one free throw', 'Make both free throws'],\n",
    "          'Probabilty': [0.2, 0.5, 0.1]}).set_index('Outcome')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<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>Probabilty</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Outcome</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Miss both free throws</th>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Make exactly one free throw</th>\n",
       "      <td>0.5</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Make both free throws</th>\n",
       "      <td>0.1</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                             Probabilty\n",
       "Outcome                                \n",
       "Miss both free throws               0.2\n",
       "Make exactly one free throw         0.5\n",
       "Make both free throws               0.1"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basketball_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "False"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "basketball_df['Probabilty'].sum() == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [],
   "source": [
    "creatures_df = DataFrame({'Type of Earth Creature': ['Chickens', 'Cows', 'Humans'], '#': [97, 47, 77]}).set_index('Type of Earth Creature')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "\n",
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       "        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>#</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Type of Earth Creature</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Chickens</th>\n",
       "      <td>97</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cows</th>\n",
       "      <td>47</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Humans</th>\n",
       "      <td>77</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                         #\n",
       "Type of Earth Creature    \n",
       "Chickens                97\n",
       "Cows                    47\n",
       "Humans                  77"
      ]
     },
     "execution_count": 31,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "creatures_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [],
   "source": [
    "creatures_df['Estimated Probabilty'] = creatures_df['#'] / creatures_df['#'].sum()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "creatures_df = creatures_df[['Estimated Probabilty']]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Estimated Probabilty</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Type of Earth Creature</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>Chickens</th>\n",
       "      <td>0.438914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Cows</th>\n",
       "      <td>0.212670</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Humans</th>\n",
       "      <td>0.348416</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                        Estimated Probabilty\n",
       "Type of Earth Creature                      \n",
       "Chickens                            0.438914\n",
       "Cows                                0.212670\n",
       "Humans                              0.348416"
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "creatures_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "creatures_df['Estimated Probabilty'].sum() == 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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