{
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   "metadata": {},
   "source": [
    "# 03 Probability with discrete random variable example"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<iframe width=\"700\" height=\"400\" src=\"https://www.youtube.com/embed/d2STHFVHGAg/\" frameborder=\"0\" allowfullscreen></iframe>\n"
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       "<IPython.core.display.HTML object>"
      ]
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   ],
   "source": [
    "%%html\n",
    "<iframe width=\"700\" height=\"400\" src=\"https://www.youtube.com/embed/d2STHFVHGAg/\" frameborder=\"0\" allowfullscreen></iframe>"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "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/example-analyzing-discrete-probability-distribution?modal=1)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "![Probability with discrete random variable example fig 1](./imgs/09-03-01.png)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = DataFrame({'X = # of packs': ['P(X)'], '1': [0.2]}).set_index('X = # of packs')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
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       "\n",
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       "        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>1</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X = # of packs</th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P(X)</th>\n",
       "      <td>0.2</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  1\n",
       "X = # of packs     \n",
       "P(X)            0.2"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['2'] = (1 - df['1']) * 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
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       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X = # of packs</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P(X)</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.16</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  1     2\n",
       "X = # of packs           \n",
       "P(X)            0.2  0.16"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['3'] = (1 - (df['1'] + df['2'])) * 0.2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
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       "      <th>3</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X = # of packs</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P(X)</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.128</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "                  1     2      3\n",
       "X = # of packs                  \n",
       "P(X)            0.2  0.16  0.128"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['4'] = (1 - (df['1'] + df['2'] + df['3']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
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       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>X = # of packs</th>\n",
       "      <th></th>\n",
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       "      <th></th>\n",
       "      <th></th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>P(X)</th>\n",
       "      <td>0.2</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.128</td>\n",
       "      <td>0.512</td>\n",
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      ],
      "text/plain": [
       "                  1     2      3      4\n",
       "X = # of packs                         \n",
       "P(X)            0.2  0.16  0.128  0.512"
      ]
     },
     "execution_count": 25,
     "metadata": {},
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   "source": [
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "df['Total'] = df.sum(axis=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
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       "      <th>4</th>\n",
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       "      <th>X = # of packs</th>\n",
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       "      <th>P(X)</th>\n",
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       "      <td>0.128</td>\n",
       "      <td>0.512</td>\n",
       "      <td>1.0</td>\n",
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      "text/plain": [
       "                  1     2      3      4  Total\n",
       "X = # of packs                                \n",
       "P(X)            0.2  0.16  0.128  0.512    1.0"
      ]
     },
     "execution_count": 27,
     "metadata": {},
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    "df"
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  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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