mikk-c/exercise_2_4.ipynb

## exercise_2_4.ipynb
{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Load the data\n",
    "df = pd.DataFrame(data = ((1, 0.1), (2, 0.15), (3, 0.2), (4, 0.21), (5, 0.17), (6, 0.09), (7, 0.06), (8, 0.02)), columns = (\"outcome\", \"p\"))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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oqARARERDJQAiIhoqARAR0VAJgIiIhqoVAJLmSVonaVDS5W3WT5J0e7n+EUkzyvYZkl4qJ35fJemayjYnSlpTbvPlkSaFj4iIvaNjAEiaACwFzgJmA+dLmt3S7WLgedtHA1cBV1bWPW17Tvn4g0r7V4DFwKzyMW/3dyMiIkarzhHAXGDQ9nrbr1DM7Tu/pc984KZy+S7g9F39RS/pKOBQ2w+VcwffDJwz6uojImK31QmAXqB6Z8RQ2da2j+0dwM+AKeW6mZIel/RtSe+v9B/qMGZEROxFde4EbveXvGv2eRaYbvs5SScCfyPp3TXHLAaWFlOcKmL69Ok1yo2IiDrqHAEMAdX7racCm0fqI+lA4DBgq+2XbT8HYPtR4GngmLL/1A5jUm63zHaf7b6enp4a5UZERB11AmAlMEvSTEkTgYVAf0uffmBRubwAuN+2JfWUHyIj6Z0UH/aut/0s8KKkk8vPCi4E7hmD/YmIiJo6ngKyvUPSpcAKYAJwve21kpYAA7b7geuAr0kaBLZShATAacASSTuAXwF/YHtrue4S4EbgYODe8hEREeOk1reB2l4OLG9pu6KyvB04t812fwX81QhjDgDHjabYiIgYO7kTOCKioRIAERENlQCIiGioBEBEREMlACIiGioBEBHRUAmAiIiGSgBERDRUAiAioqESABERDZUAiIhoqARARERDJQAiIhoqARAR0VAJgIiIhkoAREQ0VK0AkDRP0jpJg5Iub7N+kqTby/WPSJpRtp8h6VFJa8qfH6xs82A55qry8bax2qmIiOis44xg5Zy+S4EzKCZzXymp3/aTlW4XA8/bPlrSQuBK4Dzgp8Dv2t4s6TiKaSV7K9tdUM4MFhER46zOEcBcYND2etuvALcB81v6zAduKpfvAk6XJNuP295ctq8FJkuaNBaFR0TEnqkTAL3AM5XnQ+z8V/xOfWzvAH4GTGnp8x+Ax22/XGm7oTz983lJGlXlERGxR+oEQLs3Zo+mj6R3U5wW+k+V9RfYPh54f/n4eNsXlxZLGpA0sGXLlhrlRkREHXUCYAiYVnk+Fdg8Uh9JBwKHAVvL51OBu4ELbT89vIHtTeXPF4FbKE41vY7tZbb7bPf19PTU2aeIiKihTgCsBGZJmilpIrAQ6G/p0w8sKpcXAPfbtqS3An8HfNb23w93lnSgpCPL5YOAjwBP7NmuRETEaHQMgPKc/qUUV/A8Bdxhe62kJZLOLrtdB0yRNAhcBgxfKnopcDTw+ZbLPScBKyStBlYBm4C/HMsdi4iIXet4GSiA7eXA8pa2KyrL24Fz22z3ReCLIwx7Yv0yIyJirNUKgIiI2H2beqd17jRKvZue6dypg3wVREREQyUAIiIaKgEQEdFQCYCIiIZKAERENFQCICKioRIAERENlQCIiGioBEBEREMlACIiGioBEBHRUAmAiIiGSgBERDRUAiAioqESABERDVUrACTNk7RO0qCky9usnyTp9nL9I5JmVNZ9tmxfJ+nDdceMiIi9q2MASJoALAXOAmYD50ua3dLtYuB520cDVwFXltvOpphD+N3APOBqSRNqjhkREXtRnSOAucCg7fW2XwFuA+a39JkP3FQu3wWcLkll+222X7b9Q2CwHK/OmBERsRfVmRKyF6jOPTYEvG+kPrZ3SPoZMKVsf7hl295yudOYAEhaDCwun/5C0roaNY/GkcBPO/aSxvhlR21/qLNejZA663lj1Zn/Q3XtjTrf0a6xTgC0exXX7DNSe7sjj9Yxi0Z7GbBsVwXuCUkDtvv21vhjZX+oc3+oEVLnWEudY2s866xzCmgIqM5oPBXYPFIfSQcChwFbd7FtnTEjImIvqhMAK4FZkmZKmkjxoW5/S59+YFG5vAC437bL9oXlVUIzgVnAd2uOGRERe1HHU0DlOf1LgRXABOB622slLQEGbPcD1wFfkzRI8Zf/wnLbtZLuAJ4EdgCfsv0rgHZjjv3u1bLXTi+Nsf2hzv2hRkidYy11jq1xq1PFH+oREdE0uRM4IqKhEgAREQ2VAIiIaKgEwD5I0rGSTpf0lpb2ed2qqR1JcyWdVC7PlnSZpN/udl2dSLq52zV0IunU8vd5ZrdrqZL0PkmHlssHS/qvkr4p6UpJh3W7vmGS/lDStM49u0fSREkXSvpQ+fyjkv6XpE9JOmhcasiHwAVJn7B9wz5Qxx8CnwKeAuYAf2T7nnLdY7b/dTfrGybpCxTf5XQgcB/FndwPAh8CVtj+Uveq+zVJrZcXC/gt4H4A22ePe1FtSPqu7bnl8icp/g3cDZwJfNP2n3WzvmGS1gLvKa8OXAZso/z6l7L933e1wFL5bQS/BJ4GbgXutL2lu1XtTNI3KP7/vAl4AXgL8NcUv0vZXrSLzceG7TyKENzY7RrKOtYAbymXZwADFCEA8Hi362upc0L5j/fnwKFl+8HA6m7XV6nzMeDrwG8CHyh/Plsuf6Db9VXqfLyyvBLoKZffDKzpdn2V2p6q/m5b1q3qdn3V3yfFGY4zKS5T3wL8b4r7lQ7pdn1ljavLnwcCPwYmlM81Xv+H6nwVxBuGpNUjrQJ+Yzxr2YUJtn8BYHuDpN8E7pL0Dtp/tUa37HBxT8c2SU/b/jmA7Zckvdbl2qr6gD8CPgd8xvYqSS/Z/naX62p1gKTDKd605PKvVdu/lLSju6Xt5InK0fL3JPXZHpB0DPBqt4ursO3XgG8B3ypPqZwFnA/8D6Cnm8WVDihvhH0zxR9Sw9+gMAkYl1NAjQoAijf5DwPPt7QL+IfxL6etH0maY3sVgO1fSPoIcD1wfHdL28krkt5kextw4nBjeR54nwmA8k3gKkl3lj9/zL757/4w4FGKf4uW9C9s/6j8HGhfCv7fB/5c0p9QfGHZQ5Keofhyx9/vamU72+l3ZvtVim8b6Jd0cHdKep3rgO9THEl/DrhT0nrgZIpvSN7rGvUZgKTrgBtsf6fNultsf7QLZbXWMZXir+sftVl3iu2/70JZryNpku2X27QfCRxle00XyupI0u8Ap9j+L92upQ5JbwJ+w8XXqe8zJB0CvJMiTIds/7jLJe1E0jG2/7HbdXQi6e0AtjdLeivFZ2gbbX93XF6/SQEQERG/lstAIyIaKgEQEdFQCYCIDiRdNHyuNuKNJAEQ0dlFQAIg3nDyIXA0kqTLgP9YPv0q8DfA39o+rlz/aYo7M58AbgQ2AS8B/wY4Dvhziuu3X6a4c/NV4CsU9x3sAC6z/YCki4BzKC71Ow74n8BE4OPltr9te6ukfwkspbg+fRvwSdvf33u/gYgcAUQDSToR+ATF11ecDHwSOLxdX9t3UdyNfYHtOcCvgNsp7s5+D8Vley9RfHUDto+nuNnoJkmTy2GOAz4KzAW+BGyz/V7gIeDCss8y4D/bPhH4NHD1WO5zRDv74g0xEXvbqcDdtn8JIOmvgffX3PZfAc/aXgkwfAe0pFOBvyjbvi/pn4Bjym0esP0i8GL5HTXfLNvXACeUN3v9W4obgYZfZ9Ie7F9ELQmAaKJ2d9a+lZ2PiCe36TO8bbvzpru6W7d6w9xrleevUfwfPAB4oTzCiBg3OQUUTfT/gHMkvUnSm4F/B9wLvE3SFEmTgI9U+r8IHFIufx94e+VrsA+RdGA55gVl2zHAdGBdnWLKo4gfSjq33F6S3rOnOxnRSQIgGsf2YxQf7H4XeAT4anlKZ0n5/G8p3uiH3QhcI2kVxYe55wF/Iel7FF+FPZninP0ESWsoPiO4qN1XZezCBcDF5Zhrgfm7vYMRNeUqoIiIhsoRQEREQyUAIiIaKgEQEdFQCYCIiIZKAERENFQCICKioRIAERENlQCIiGio/w8KEZzdhUUYrgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Probability mass function\n",
    "df.plot(kind = \"bar\", x = \"outcome\", y = \"p\", color = \"#e41a1c\")\n",
    "plt.savefig(\"pmf.png\")\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEDCAYAAAAlRP8qAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADh0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uMy4xLjMsIGh0dHA6Ly9tYXRwbG90bGliLm9yZy+AADFEAAAUV0lEQVR4nO3df5DcdX3H8ef7kkAQotbkoDRHPIqkJeYH4iVilQkdaAqUIbVSA1gVKuQPjTCk7UxaGNumw4z9NRlEKs2oFRAMPywQnVjUAmoRQg5IwBDJBES5oHgNAlHEJOTdP3aTLpe9272wl7378HzMZLL7/X72u6/b3L3yve9+P9+NzESSNPZ1tDuAJKk1LHRJKoSFLkmFsNAlqRAWuiQVwkKXpEKMb9cTT5kyJbu7u9v19JI0Jj344IP/m5md9da1rdC7u7vp7e1t19NL0pgUET8abJ2HXCSpEBa6JBXCQpekQrTtGHo9O3fupK+vj5dffrndUYo3ceJEurq6mDBhQrujSGqRUVXofX19TJo0ie7ubiKi3XGKlZls27aNvr4+jj766HbHkdQiDQ+5RMQXIuJnEfH9QdZHRHw6IrZExCMRccL+hnn55ZeZPHmyZT7CIoLJkyf7m5BUmGaOoX8ROG2I9acDx1b/LAY++1oCWeYHhq+zVJ6GhZ6Z3wGeG2LIQuC6rLgfeHNEHNmqgCV76qmnmDlzZsMxN9544977vb29XHzxxSMdTdIY1Ipj6FOBp2vu91WX/WTgwIhYTGUvnmnTpjXc8NapR7Ug3v+buvXpxoNGmT2Fft555wHQ09NDT09Pm1NJr1+t7iVoXTe14rTFer+71/0YpMxcmZk9mdnT2Vl35uqocN111zF79mzmzJnDhz70Ic4//3xuvfXWvesPO+wwAO655x7mz5/PBz7wAaZPn86yZcu44YYbmDdvHrNmzeKJJ54AGPTxtZ566ilOOukkTjjhBE444QS+973vAbBs2TK++93vcvzxx7NixQruuecezjzzTHbv3k13dzfPP//83m287W1v49lnn6W/v5/3v//9zJ07l7lz53LvvfeOyOskaXRpRaH3AbX/ZXUBz7Rgu22xceNGrrjiCu666y42bNjAlVdeOeT4PWMeffRRrr/+ejZv3swDDzzAhRdeyFVXXdX08x5++OF885vf5KGHHuKmm27ae1jlU5/6FCeddBLr16/n0ksv3Tu+o6ODhQsXcttttwGwdu1auru7OeKII7jkkku49NJLWbduHV/5yle48MIL9+OVkDTWtOKQy2pgSUSsAt4FvJCZ+xxuGSvuuusuzj77bKZMmQLAW97yliHHz507lyOPrLxlcMwxx7BgwQIAZs2axd1339308+7cuZMlS5awfv16xo0bx+bNmxs+ZtGiRSxfvpwLLriAVatWsWjRIgC+9a1v8dhjj+0d9+KLL7J9+3YmTZrUdB5JY0/DQo+ILwMnA1Miog/4W2ACQGZeA6wBzgC2AC8BF4xU2AMhM/c5A2T8+PHs3r177/odO3bsXXfwwQfvvd3R0bH3fkdHB7t27Wr4+D1WrFjBEUccwYYNG9i9ezcTJ05smPXd7343W7Zsob+/n9tvv53LL78cgN27d3PfffdxyCGHDOdLl9puNB+fHguaOcvl3Mw8MjMnZGZXZn4+M6+pljnVs1s+npnHZOaszBzTl1A85ZRTuPnmm9m2bRsAzz33HN3d3Tz44IMA3HHHHezcuXNY22zm8S+88AJHHnkkHR0dXH/99bzyyisATJo0ie3bt9fdbkTwvve9j6VLl3LccccxefJkABYsWMBnPvOZvePWr18/rLySxiav5TLA29/+di677DLmz5/PnDlzWLp0KRdddBHf/va3mTdvHmvXruXQQw8d1jabefzHPvYxrr32Wk488UQ2b968d8zs2bMZP348c+bMYcWKFfs8btGiRXzpS1/ae7gF4NOf/jS9vb3Mnj2bGTNmcM011wzzVZA0FkVm3RNSRlxPT08OvB76pk2bOO6449qS5/XI11ujzVg45NLujBHxYGbWPXfZPXRJKoSFLkmFsNAlqRCjrtDbdUz/9cbXWSrPqCr0iRMnsm3bNstmhO25Hnoz57pLGjtG1QdcdHV10dfXR39/f7ujFG/PJxZJKseoKvQJEyb4CTqStJ9G1SEXSdL+s9AlqRCj6pCLpJHR7tmNOjDcQ5ekQljoklQIC12SCmGhS1IhLHRJKoSFLkmFsNAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAg/gk56DfxoN40m7qFLUiGaKvSIOC0iHo+ILRGxrM76aRFxd0Q8HBGPRMQZrY8qSRpKw0KPiHHA1cDpwAzg3IiYMWDY5cDNmfkO4Bzg31odVJI0tGb20OcBWzLzyczcAawCFg4Yk8Abq7ffBDzTuoiSpGY086boVKD2XZo+4F0Dxvwd8I2I+ARwKHBqS9JJkprWzB561FmWA+6fC3wxM7uAM4DrI2KfbUfE4ojojYje/v7+4aeVJA2qmULvA2rPzepi30MqHwVuBsjM+4CJwJSBG8rMlZnZk5k9nZ2d+5dYklRXM4W+Djg2Io6OiIOovOm5esCYHwOnAETEcVQK3V1wSTqAGhZ6Zu4ClgB3ApuonM2yMSKWR8RZ1WF/AVwUERuALwPnZ+bAwzKSpBHU1EzRzFwDrBmw7JM1tx8D3tPaaJKk4XCmqCQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCmGhS1IhLHRJKoSFLkmFsNAlqRDj2x1Aqmfr1KNavs2pW59u+Tal0cQ9dEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCtFUoUfEaRHxeERsiYhlg4z5QEQ8FhEbI+LG1saUJDXScGJRRIwDrgb+AOgD1kXE6sx8rGbMscBfA+/JzJ9HxOEjFViSVF8ze+jzgC2Z+WRm7gBWAQsHjLkIuDozfw6QmT9rbUxJUiPNFPpUoHbOdF91Wa3pwPSIuDci7o+I01oVUJLUnGau5RJ1lmWd7RwLnAx0Ad+NiJmZ+fyrNhSxGFgMMG3atGGHlSQNrpk99D6g9kpJXcAzdcbckZk7M/OHwONUCv5VMnNlZvZkZk9nZ+f+ZpYk1dFMoa8Djo2IoyPiIOAcYPWAMbcDvw8QEVOoHIJ5spVBJUlDa1jombkLWALcCWwCbs7MjRGxPCLOqg67E9gWEY8BdwN/lZnbRiq0JGlfTV0PPTPXAGsGLPtkze0Ellb/SJLawJmiklQIC12SCmGhS1IhLHRJKoSFLkmFsNAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCjG+3QF0YG2delTLtzl169Mt36ak4XMPXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBWiqUKPiNMi4vGI2BIRy4YYd3ZEZET0tC6iJKkZDQs9IsYBVwOnAzOAcyNiRp1xk4CLgbWtDilJaqyZPfR5wJbMfDIzdwCrgIV1xv0D8E/Ayy3MJ0lqUjOFPhWonQrYV122V0S8AzgqM7/WwmySpGFoptCjzrLcuzKiA1gB/EXDDUUsjojeiOjt7+9vPqUkqaFmCr0PqL0ASBfwTM39ScBM4J6IeAo4EVhd743RzFyZmT2Z2dPZ2bn/qSVJ+2im0NcBx0bE0RFxEHAOsHrPysx8ITOnZGZ3ZnYD9wNnZWbviCSWJNXVsNAzcxewBLgT2ATcnJkbI2J5RJw10gElSc1p6vK5mbkGWDNg2ScHGXvya48lSRouZ4pKUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklQIC12SCmGhS1IhLHRJKoSFLkmFsNAlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqxPh2ByjF1qlHtXybU7c+3fJtSiqXe+iSVAgLXZIKYaFLUiEsdEkqhIUuSYVoqtAj4rSIeDwitkTEsjrrl0bEYxHxSET8d0S8tfVRJUlDaVjoETEOuBo4HZgBnBsRMwYMexjoyczZwK3AP7U6qCRpaM3soc8DtmTmk5m5A1gFLKwdkJl3Z+ZL1bv3A12tjSlJaqSZQp8K1M5w6asuG8xHga+/llCSpOFrZqZo1FmWdQdG/BnQA8wfZP1iYDHAtGnTmowoSWpGM3vofUDtvPYu4JmBgyLiVOAy4KzM/HW9DWXmyszsycyezs7O/ckrSRpEM4W+Djg2Io6OiIOAc4DVtQMi4h3Av1Mp85+1PqYkqZGGhZ6Zu4AlwJ3AJuDmzNwYEcsj4qzqsH8GDgNuiYj1EbF6kM1JkkZIU1dbzMw1wJoByz5Zc/vUFueSJA2TM0UlqRAWuiQVwkKXpEJY6JJUCAtdkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYVo6gMu2m3r1KMaDxqGqVufbun2JGk0cA9dkgphoUtSISx0SSqEhS5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqhIUuSYWw0CWpEBa6JBXCQpekQljoklSIpgo9Ik6LiMcjYktELKuz/uCIuKm6fm1EdLc6qCRpaA0LPSLGAVcDpwMzgHMjYsaAYR8Ffp6ZbwNWAP/Y6qCSpKE1s4c+D9iSmU9m5g5gFbBwwJiFwLXV27cCp0REtC6mJKmRZj5TdCpQ+yGcfcC7BhuTmbsi4gVgMvC/tYMiYjGwuHr3FxHx+P6EHsKUgc9ZV/v/rzFna42FnM1lBHM2p6ycw8v41sFWNFPo9Z4p92MMmbkSWNnEc+6XiOjNzJ6R2n6rmLO1xkLOsZARzNlqBzpnM4dc+oCjau53Ac8MNiYixgNvAp5rRUBJUnOaKfR1wLERcXREHAScA6weMGY18JHq7bOBuzJznz10SdLIaXjIpXpMfAlwJzAO+EJmboyI5UBvZq4GPg9cHxFbqOyZnzOSoYcwYodzWsycrTUWco6FjGDOVjugOcMdaUkqgzNFJakQFrokFcJCl6RCWOgHQET8bkScEhGHDVh+WrsyDRQR8yJibvX2jIhYGhFntDtXIxFxXbszNBIR762+ngvanaVWRLwrIt5YvX1IRPx9RHw1Iv4xIt7U7nx7RMTFEXFU45HtFREHRcSHI+LU6v3zIuIzEfHxiJhwQDKU+KZoRFyQmf/R7hxQ+WYEPg5sAo4HLsnMO6rrHsrME9qZr5rjb6lcq2c88E0qM4HvAU4F7szMK9qX7v9FxMDTZQP4feAugMw864CHqiMiHsjMedXbF1H5978NWAB8NTM/1c58e0TERmBO9Uy2lcBLVC/dUV3+J20NWFWdef5L4Angy8Atmdnf3lT7iogbqPwMvQF4HjgM+E8qr2dk5keGeHhrZGZxf4AftztDTZZHgcOqt7uBXiqlDvBwu/PVZBxX/UZ8EXhjdfkhwCPtzleT8yHgS8DJwPzq3z+p3p7f7nw1OR+uub0O6KzePhR4tN35arJtqn1tB6xb3+58ta8nlaMJC6icIt0P/BeVuS+T2p2vJucj1b/HA88C46r340D9HDUz9X9UiohHBlsFHHEgszQwLjN/AZCZT0XEycCtEfFW6l8yoR12ZeYrwEsR8URmvgiQmb+KiN1tzlarB7gEuAz4q8xcHxG/ysxvtznXQB0R8RtUSiiyujeZmb+MiF3tjfYq36/5bXZDRPRkZm9ETAd2tjtcjczM3cA3gG9UD1+cDpwL/AvQ2c5wNTqqky8PpbJztGfG/MHAATnkMmYLnUpp/yHw8wHLA/jegY8zqJ9GxPGZuR4gM38REWcCXwBmtTfaXjsi4g2Z+RLwzj0Lq8dRR02hV3+oV0TELdW/n2V0fg+/CXiQyvdiRsRvZuZPq++hjJb/xAEuBK6MiMupXEDqvoh4msqF9i5sa7JXe9Vrlpk7qcxOXx0Rh7QnUl2fB35A5bfdy4BbIuJJ4EQqV6kdcWP2GHpEfB74j8z8nzrrbszM89oQax8R0UVlD/indda9JzPvbUOsgTkOzsxf11k+BTgyMx9tQ6yGIuKPgPdk5t+0O0szIuINwBGZ+cN2Z6kVEZOA36byn2NfZj7b5kivEhHTM3Nzu3M0IyJ+CyAzn4mIN1N5H+rHmfnAAXn+sVrokqRX87RFSSqEhS5JhbDQ9boSEefvOc4plcZC1+vN+YCFriL5pqjGvIhYCvx59e7ngNuBr2XmzOr6v6Qya+/7wBeBrcCvgHcDM4ErqZw7/Gsqs/p2Ap+lct77LmBpZt4dEecDf0zltLSZwL8CBwEfqj72jMx8LiKOAa6mcn70S8BFmfmDkXsFpAr30DWmRcQ7gQuoXK7gROAi4Dfqjc3MW6nM1P1gZh4PvALcRGXm7hwqp5j9ispUfTJzFpXJK9dGxMTqZmYC5wHzgCuAlzLzHcB9wIerY1YCn8jMdwJ/CfxbK79maTCjcVKGNBzvBW7LzF8CRMR/Aic1+djfAX6SmesA9syQjYj3AldVl/0gIn4ETK8+5u7M3A5sr15j5KvV5Y8Cs6uTh36PyqSSPc9z8Gv4+qSmWega6+rNvHwzr/7tc2KdMXseW++Y41CzOWsnYO2uub+bys9TB/B89TcA6YDykIvGuu8AfxwRb4iIQ4H3AV8HDo+IyRFxMHBmzfjtwKTq7R8Av1Vz2eBJETG+us0PVpdNB6YBjzcTprqX/8OI+NPq4yMi5rzWL1JqhoWuMS0zH6LyRucDwFrgc9VDKMur979Gpbj3+CJwTUSsp/Lm5iLgqojYQOXSwROpHPMeFxGPUjnGfn69SyMM4YPAR6vb3Ags3O8vUBoGz3KRpEK4hy5JhbDQJakQFrokFcJCl6RCWOiSVAgLXZIKYaFLUiEsdEkqxP8B1UpU534GEZAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Calcualte the cumulative sum and plot it as cumulative distribution\n",
    "df[\"cumulative\"] = df[\"p\"].cumsum()\n",
    "df.plot(kind = \"bar\", x = \"outcome\", y = \"cumulative\", color = \"#e41a1c\")\n",
    "plt.savefig(\"cumulative.png\")\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}
	{
	"cells": [
	{
	"cell_type": "code",
	"execution_count": 1,
	"metadata": {},
	"outputs": [],
	"source": [
	"import pandas as pd\n",
	"import matplotlib.pyplot as plt"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 2,
	"metadata": {},
	"outputs": [],
	"source": [
	"# Load the data\n",
	"df = pd.DataFrame(data = ((1, 0.1), (2, 0.15), (3, 0.2), (4, 0.21), (5, 0.17), (6, 0.09), (7, 0.06), (8, 0.02)), columns = (\"outcome\", \"p\"))"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 3,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"needs_background": "light"
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"# Probability mass function\n",
	"df.plot(kind = \"bar\", x = \"outcome\", y = \"p\", color = \"#e41a1c\")\n",
	"plt.savefig(\"pmf.png\")\n",
	"plt.show()"
	]
	},
	{
	"cell_type": "code",
	"execution_count": 4,
	"metadata": {},
	"outputs": [
	{
	"data": {
	"image/png": 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\n",
	"text/plain": [
	"<Figure size 432x288 with 1 Axes>"
	]
	},
	"metadata": {
	"needs_background": "light"
	},
	"output_type": "display_data"
	}
	],
	"source": [
	"# Calcualte the cumulative sum and plot it as cumulative distribution\n",
	"df[\"cumulative\"] = df[\"p\"].cumsum()\n",
	"df.plot(kind = \"bar\", x = \"outcome\", y = \"cumulative\", color = \"#e41a1c\")\n",
	"plt.savefig(\"cumulative.png\")\n",
	"plt.show()"
	]
	}
	],
	"metadata": {
	"kernelspec": {
	"display_name": "Python 3",
	"language": "python",
	"name": "python3"
	},
	"language_info": {
	"codemirror_mode": {
	"name": "ipython",
	"version": 3
	},
	"file_extension": ".py",
	"mimetype": "text/x-python",
	"name": "python",
	"nbconvert_exporter": "python",
	"pygments_lexer": "ipython3",
	"version": "3.7.6"
	}
	},
	"nbformat": 4,
	"nbformat_minor": 4
	}