Statistical_Thinking_in_Python_course_1.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Statistical Thinking in Python (Part 1)\n",
    "## Graphical Exploratory Data Analysis\n",
    "Exploring your data is curucial step in your analysis.\n",
    "* Organizing \n",
    "* Plotting \n",
    "* Computing a few numerical summaries\n",
    "\n",
    "We are going to explore the 2008 US swing state election result which is at country level in each of the three major swing states of Pennslvanie, Ohio, and Florida.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "#loading thelibraries\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "#seaborn is excellent matplotlib based statistical data visulation package\n",
    "import seaborn as sns\n",
    "sns.set()\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   state              county  total_votes  dem_votes  rep_votes  dem_share\n",
      "0     PA         Erie County       127691      75775      50351      60.08\n",
      "1     PA     Bradford County        25787      10306      15057      40.64\n",
      "2     PA        Tioga County        17984       6390      11326      36.07\n",
      "3     PA       McKean County        15947       6465       9224      41.21\n",
      "4     PA       Potter County         7507       2300       5109      31.04\n",
      "5     PA        Wayne County        22835       9892      12702      43.78\n",
      "6     PA  Susquehanna County        19286       8381      10633      44.08\n",
      "7     PA       Warren County        18517       8537       9685      46.85\n",
      "8     OH    Ashtabula County        44874      25027      18949      56.94\n",
      "9     OH         Lake County       121335      60155      59142      50.46\n",
      "10    PA     Crawford County        38134      16780      20750      44.71\n",
      "11    OH        Lucas County       219830     142852      73706      65.99\n",
      "12    OH       Fulton County        21973       9900      11689      45.88\n",
      "13    OH       Geauga County        51102      21250      29096      42.23\n",
      "14    OH     Williams County        18397       8174       9880      45.26\n"
     ]
    }
   ],
   "source": [
    "swing_state = pd.read_csv('data/2008_swing_states.csv')\n",
    "print(swing_state.head(15))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We take the Democratic share of the vote in the counties of all the three swing state and plot them as a histogram. We are interested in the fraction of the vote to Brack Obama in the county. \n",
    "\n",
    "We can specified where the edge of the bars of histigrams are, the bin edges, and use the bins keywords arguments pass that to the plt.hist."
   ]
  },
  {
   "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": [
    "#we are goint to use  different binning\n",
    "bin_edges = [0, 10,20,30,40,50,60,70,80,90,100]\n",
    "_ = plt.hist(swing_state['dem_share'], bins=bin_edges)\n",
    "#labeling the plot\n",
    "_ = plt.xlabel('Percent of vote for Obama')\n",
    "_ = plt.ylabel('Number of countries')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the plot below, We have been use the bins=20 which create 20 evenly spaced bin by the default setting. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "scrolled": false
   },
   "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": [
    "#We can specified where the edge of the bars of histigrams are using the bins keyword\n",
    "# 20 evenly spaced bins will create\n",
    "_ = plt.hist(swing_state['dem_share'], bins =20)\n",
    "#labeling the plot\n",
    "_ = plt.xlabel('Percent of vote for Obama')\n",
    "_ = plt.ylabel('Number of counties')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bee swarm plots\n",
    "Here is the bee swarm plot of the vote totals in three  swing states.\n",
    "\n",
    "Each point in the plot represent the share of the vote Obama got into single county. The y-axis gives us the quantitative information.\n",
    "\n",
    "* We can clearly see that  Obama got less than 50% of the vote in the majority of couties in each the three swing states."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.swarmplot(x='state', y='dem_share', data=swing_state)\n",
    "plt.xlabel('state')\n",
    "plt.ylabel('percent of vote for Obama')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Empirical cumulative distribution functions (ECDF)\n",
    "\n",
    "We are going to plot ECDF for the percentage of the vote for the Obama. The x-axis is a percent of the vote that vote for Obama. The y-axis is the fraction of data point that has a value smaller than the corresponding x-value."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "scrolled": true
   },
   "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": [
    "#We can use np.sort() to generate our x-data\n",
    "x = np.sort(swing_state['dem_share'])\n",
    "#y-axis is evenly speaced data point with a max 1.\n",
    "y = np.arange(1, len(x) +1)/len(x)\n",
    "_ = plt.plot(x,y, marker ='.', linestyle='none')\n",
    "plt.xlabel('Percent of Vote for Obama')\n",
    "plt.ylabel('ECDF')\n",
    "#Keep the data off from plot edge\n",
    "plt.margins(0.02) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "*75% of counties in swing states had 50% or less of its people vote for Obama*"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array(['PA', 'OH', 'FL'], dtype=object)"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "swing_state['state'].unique()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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88Qo333zLaZ+fnt6Xb7/92nWS3erVq+jb91KPxSdaNufE9a6937o2xhm6Tm5Sb7d5uF37irCfCMd+sCuqNIKyCpuPIxf+RkYUXvbEE0+zdOkL3HTTdVgsFtq2vYAHH3yMPn368a9/LW30uUlJydx00x+ZNes27HY7KSndmTfv7A43Eq2PY+7NRmKFiVWFYdfAolvp3mMsllrzDM4THg0vnfAomj85j6JGczrnobnEKedReM7ZxFm98ysyf3yTnJBAQg2T6q79aBM5kJLCMFIuinQrL9U+a+Jcyk4t+evpC3IehRDCq/aU5vNyXCR2DawKppVZeOX/CrEbBVgtutuxv0nx4TIvIRokcxRCtEBGQRa7y/Idx5FqGnYNfrIr7IaJUmAYJrv2Ffk6TNFMSKIQooXJ2rOBT755juBDWVgVaIBVt3Jx5/5YdMfyWF3XZC5CnDEpPQnRguQU5/L8njXYI4OxqmDGHSmh6qKedO8xFrM0AsVhAJrtxKTwCRlRCNGC7C7Kxo7pKjeVW3SuiryYxPAEdu0rci3+UKaS0pM4Y5IohGghcopzOVqUi0WBphRWBYkVNlRlKeBYBiulJ3E2pPTkZQcP5jN16rV07ux+8ld4eDijRo1hzJjxZ/Q6GRm/sWrV+8yf//Apr3/XXX9i5co1HotZND85xbks/ulFx7GkCi4rqaBPSRUJNs2tJY2q87cQZ0ISxXnQoUMUr7223O2+BQseadJrpKZezLx5F3swKtGSOBv7KU3DRBFhN0lsn0JQv0luO7Drlp5kSaw4E15NFGvWrOGf//wndrudm2++mRtuuMHt+q+//spDDz2EzWajY8eOPPPMM1xwwQXeDKlB2cf3knEkyycnddVtJT5nzj2EhoYybtyVpKRczNGjR7jzztm8/vq/ePHFl8nMzGDhwscASErq5nqdnJwsFi16hoqKCoqKjnHTTX9g0qTJ5/VzEedfTnEuxyqLsKBjKMNRcqpSBA2b5NaSJiwkAL0mkcgObNEUXksUBQUFLFq0iA8++IDAwECmTJlC//79SUo6+YO7YMECZs+ezfDhw1m4cCGvvPIKc+bM8VZIDcopzmXx1qXYTTtW3crs9Ns8miyOHCnkD3+Y5ro9cuRo18fOVuJLl75GeHgEf/vbU7z66jLuvPO/OX78ODfcMJ0+ffrx00+bXc95/PGHueuuOVx66QBee+1l17U1az7i5ptvoV+/yzhwYD9/+MM0SRQtXO2fXd00a0pONrpdOtUtSWQdKGbF57sxTIWua0y9MllGE+KMeW0ye+PGjQwYMICIiAhCQ0MZNWoUa9eudXuMaZqUlZUBUFFRQXCwbw7k2V2UfbJpmmlnd1G2R1/fWXpy/pk2bbrrWn2txLds+cF1vUePS9xe6/jxIo4cOcKllw4A4Oqrx7muzZp1N9XV1fz736+ybNk/qago9+jnIfyLUZDFzl8/cf3smhpE2E0Sqk5OYDvt2leE3ahp/aKUNP4TTeK1EcXhw4eJiopy3Y6Ojmb79u1uj5k3bx4zZszgiSeeICQkhHfffbdJ71Ffz5LDh3Ws1qblv9QOSXy69wsM045Ft5LaIanJr9EQi8XxOnVfT9M09ForUJzXLRbHGRbO22Fhoa7X0TSt5hAk5boeFBTgev358++hbdsLGDp0GKNGjebzz9d57PM4G7quExXV1mfvf6aaQ4zgiDPzSA6/Hs4kiSDafLKUBCtY48IxdA2LgsQKO5rFSoeL+xBc6/Ma0DOe1Rv2Yrc7Gv8N6Bnvtc+7OX09mwN/iNNricI0TbeT3ZRSbrcrKyt54IEHeO211+jZsyevvvoq9957L0uXNt5Rtbb6mgKaptnkpnkJbS5iTr8/ueYoEtpc5LHGe0bNb3F1X08phWkqevXqwzvvLGf69Fu44IJwPvzwA9LT+7ke7/zbMEyUUoSHRxATE8vXX3/NoEFD+PTTT12P++GH71m+fCUdOkTxwQfvAVBVZXOdeXE+Wa06pmn6feO15tQc7vusX06WSNG41apIqLRxa34xuUm9SenYiwvbF2GNS6UkKI6SWp9X0fFyTKVQgKkURcfLKSwM8EqczeXr2Rrj9LumgLGxsWzefLKuXlhYSHR0tOt2ZmYmQUFB9OzZE4Drr7+e5557zlvhnFbXiM4ktLnovL9vfa3E5869r9HnPPjgYzz55F9ZtuwFevTo6bp/xoyZ/PnPtxIUFEjXrsl07BjHwYP5dOp0obc/DXEeuJVIUeSEBJJQaSfBBt27jmz0LBVZ8STOhdcSxaBBg1iyZAnHjh0jJCSE9evX89hjj7muJyQkcOjQIXJyckhMTOSLL74gLS3NW+H4TMeOcfXucXjggUdcH48fP4nx4yed8phvvz2ZaPv06UefPv0ASEzsyrJlb5zy+ClTbmTKlBs9ELXwJznFuXxbuJ+wgDCsutVRIjVNEiuqQNMJGjSNPfYodm3a22CbcDlzQpwLryWKmJgY5syZw/Tp07HZbEyePJmePXsyc+ZMZs+eTVpaGk8++SR33303Sinat2/PE0884a1whGiWnKuaDNOORdOZFJJIWWUxCft3kVBpB03nyOEjPPPJVuyGeUr7cKek+HDmTk33yJkTovXx6j6K8ePHM368+87jZcuWuT4ePnw4w4cP92YIQjRrtctNyrRzIm8rI4qrHRc1HXQrWbYY7IbNrX14fYlAzpwQZ0t2Zgvhx5Iju9aUm2w1q5qqQZlYU4ejt2mPNS6VOHsU1m1bpawkvKZFJoq6K6zE+deMT9j1uZziXHYXZbu6BMxKGEP2gR+I37OLhCoTpVn4sSqRuMSeJMWEkwRSVhJe1eIShdUaSFnZCcLCLpBk4SNKKUpKTmC1Bvo6lGanbpeAWQljiPnydWJMx3xE+YUDeGVnBNlbbFi3bXXNR0hZSXhTi0sUkZFRFBUVUlp6vEnP03XHun9/11ziDAsLJTIy6vQPFG7qdgnIyPycGMOGs99rQVUI2dUdTjsfIYQntbhEYbFY6dChY5Of11o34HhLc4nTn7ia+2kWTGVgMU06F+QBCoWGiU5VuySsliqZjxDnVYtLFEI0R27N/TSd/loEvfOzSai0o9DItHfk0/Je7P++iqlXJlNWYZP5CHHeSKIQwg+4LYNVJhccO+DYJwEoTefT8l7ssUehayZlFTbGDuzs24BFqyJHoQrhB8ICwhxNH9GwoJFYXgWAQmNvaBr7iUHXkHKT8AkZUQjhYznFuazcvRpTmehoTNBjSKg+gkLHpjRWH+yIUophveIYlNZRyk3ivJNEIYSPOctOAEqZlBbuBuBgZB/ezY2qKTkp2ocHS5IQPiGlJyF87GTZCccxpjW7r9tGx5KnHB2XpeQkfEkShRA+VLvspJmKcUdKXM3+bO2TcO5vl53uwpckUQjhQ25lJw3KLTqgYU0Zyi8lEa4zJMyaMySE8AWZoxDCh5Iju2LRLNiV/WTTP91CYLfBpNgjsegadkNJ6Un4lIwohPAxVVNgqq+4JKUn4Q8kUQjhQ7uLsjGVo3eXqUFOSCAoE3t+htvxpVJ6Er4kpSchzqO6LcSTI7ti1XRHt1gFXSqqUZqONS6VFPvJ40utVik9Cd+RRCHEeVK3hfjs9NtIDE/gz23S2LX3WxIrqrmwws6m6m50tUe5HV86oGc87cMCfP0piFZKEoUQ50ndFuK7i7JJDE+gS5s4OhaVuyYk8uztsNe0D3f+kW68wpdkjkKI86B2C3EdDYtuJTmyKwCqshQATQMTaGOpljKT8CsyohDCy+q2EB8U159Lg2KIz9mBEWfDGpdKlR6AYdgx0Mmyx9DP10ELUYskCiG8rG4L8Qi7QcyG16k2bVTrAYSOu4dtnadz4Nef2G2LZZ8RJSfXCb8ipSchvCw5sitW3eooOWk6CXlZYNhAKTDt2PMziOvek69svdhnRMnmOuF3ZEQhhJclhicwOXkCW/d/R/e9mVxYfLDmiobSLHx/NJy4aFwrnOTkOuFvJFEI4WXOxn9200Z2+1Biq6pIqDSo6pDC0txEsrfYsG7bytyp6XJynfBLUnoSwstOzlGA3bn72hLAbxcMJru6A0qBYZiy81r4LUkUQnhZWEAYGqApVXPehEHQoGmYHRLRNQ1NjjgVfk5KT0J4UU5xLiszV2Eqha5wnDdRZePI4SOs+BEMU6HrGlOvTJZ5CeG3ZEQhhBftyvvBcd6EVuu8Cd1Kli0Gu+FoBohSlFXYfBuoEI2QRCGEh+QU57Ju75fkFOe67kussGFVJ8tOSW0uJHTcPcR174lF1wDQdU3KTsKvSelJCA9oqOFflzZx3LrzS3JCAkmsqCbp0rFYYpLgQPHJsyZ8GrkQpycjCiE8oL6Gf+Do45RQaWdEUTkJlYarr1PtsyaUnDUh/JwkCiE8wHmkKYCuWVwN/6xxqaDXDNx1i+M2EBYSICueRLPh1USxZs0axowZw8iRI3nrrbdOuZ6Tk8NNN93EhAkTuOWWWyguLvZmOEJ41ckjTRsvJmUdKGbF57sxTIWmyYon4f+8ligKCgpYtGgRy5cvZ9WqVbzzzjtkZWW5riul+POf/8zMmTNZvXo13bt3Z+nSpd4KRwivqn2kqVKmq/Rky9wApt3xoFpHnMqKJ9GceG0ye+PGjQwYMICIiAgARo0axdq1a5k1axYAv/76K6GhoQwbNgyA22+/nRMnTngrHCG8wnm0aVhAGFbdimHaXWdNGAVZ2HZ9c/LBms6hgE4cLajEomuYppKyk2gWvJYoDh8+TFRUlOt2dHQ027dvd93et28fHTp04P7772fnzp0kJiby4IMPeiscITyu7kqnyckTKLOVuc7Drsr5GJRR82iNsk79eWLtceyGia5rDOsVx6C0jlJ2En7Pa4nCNE00TXPdVkq53bbb7fzwww+8+eabpKWl8T//8z8sXLiQhQsXnvF7tG/fxqMxR0W19ejreYvE6VlnG+e3hfsxnCudlAGBdm7sPdF1vfLiPuT/9BEYdrBYyWubhmGUo5RjpdNFceEM7N3J63GebxKnZ/lDnF5LFLGxsWzevNl1u7CwkOjoaNftqKgoEhISSEtLA2DcuHHMnj27Se9x9Gipa4nhuWouZxJLnJ51TnFWW0HT0BRYNAtxgZ3cXss4Xu44cwKFMk0KjpSh6zrUlJw6tQ894/duFV/P86i1xqnr2ln9gu21yexBgwaxadMmjh07RkVFBevXr3fNRwCkp6dz7NgxMjIyAPjyyy/p0aOHt8IRwqOcrcNN5Rg5T06eQGJ4gttj7PkZYDpKT8o0KNn7CwoY1iuOuVPTpeQkmg2vjShiYmKYM2cO06dPx2azMXnyZHr27MnMmTOZPXs2aWlp/OMf/2D+/PlUVFQQGxvL008/7a1whPAo5wY7wLFyyVZ2ymO04DY4F8tqQKkZhDIV7cODJUmIZsWrLTzGjx/P+PHj3e5btmyZ6+NevXqxcuVKb4YghFc4jzetvcqpNqMgC3uOo/SqAQbQRq+SVU6iWZJeT0I0gXM5bHJkV2an3+b6uHbZySjIovzjp8GoBkChoXQLbTtfwtx+UnISzU+jcxTXXHON6+Ovv/7a68EI4c+cy2HX5Kxj8VbH5tBRna9oYG7CsYlOoZFp68jzxVexZrflvMcshCc0miiUOrmiaNGiRV4PRgh/1lDjv7occxM6oGFqFj6t6MUee5QcdyqarUYTRd19EEK0Zg01/qvNKMiiauNylDIw0ci7aCz7iUGX5n+iGTvjOYraSUOI1up0jf/s+Rkow4aGo+fTb7vymHrlZZRV2Ei5KFLmJ0Sz1GiiOHHiBJ999hlKKUpKSli/fr3b9ZEjR3o1OCH8SX2N/+rOT7iWxCrHaqcSI5A2FTbGDux83uMVwlMaTRRxcXG88cYbAHTs2JF///vfrmuapkmiEK1GTnEuxyqLsGgWTGXUuyQ260Ax5Zl5dAY0DQwFbS3VUm4SzV6jiaJ2YhCitard/E/XdAbF9ad/x75uo4msA8W8++460q15dArUsWoKdAsDrhhGgpSbRDN32jmKsrIyPv74YzIzMwkODiYlJYXRo0cTGBh4PuITwudqr3ZSyqRdcMQpJaf8ndv5U+g6LBiY6ByM7EvSsNFExCT5KGohPKfRVU+5ubmMHTvF61R3AAAgAElEQVSW9evXExQUBMDKlSsZPXo0Bw4cOC8BCuFrYQFhaJqGhnZKySnrQDGfbNpLdHUeVgwsGlgwaRsdi0WShGghGh1RLF68mDlz5jBx4kS3+9977z2effZZ2VshWrzazf90TXdr/pd1oJhnVmzFbpgMDi5hcgiOvk4adIju4NvAhfCgRkcUmZmZpyQJgN///vfs2bPHa0EJ4S8aa/6Xv3M7lwf8TIKlkBAqAcdKJw0NVVnqg2iF8I5GRxQWS8MtB2RfhWjpGlvpZBRk0XvvG/QMtjEy2MKqiktBD3CcaKdbscal+jh6ITyn0UQhyUC0Vqdb6eTo52THogHKJEyvpmjAncTa9mONS5X5CdGiNJooDh06xOOPP17vtYKCAq8EJIQ/aGylk1GQhVl6FKXpmKaJgc7u6hjalkSQMLC3jyMXwvMaTRQ33HBDg9emTZvm8WCE8BfOlU4oTik5lX/8dE13WJ3vqpP5saor+4lhqmysEy1Uo4li1qxZp9xXXV0teyhEi9bYSidb5oaT50wok2NGGLlmNDeOTJY+TqLFanTVU3V1Nffeey+fffaZ67677rqL++67D7vd7vXghPCFhlY6GQVZ2HZ947gbMNHIssc6HlNh81G0Qnhfo4li8eLFlJaW0qdPH9d9jz76KMXFxSxZssTrwQnhC85jTvU6G+zs+RmOVU0AaPxYncQ+I0rah4sWr9HS01dffcXKlSsJDg523RcTE8PTTz/N9ddfz5w5c7weoBDnS0PHnCZU2qjK+djRGVYPANOOpltp13sE3fOD6ZsSLWUn0aI1migCAgLckoRTmzZtZJ5CtCi1l8NadSuz029jVOcr3Cev9QCCBk1DVZZyKKATL689jt2oIDOvmE5RbSRZiBar0dKTruuUlp66w7S0tFTmKESL0tAxp67Ja6XAtKMqSwlKH8cvJRHYDROlkCNORYvXaKIYN24c8+fPp7y83HVfeXk58+fPl7MoRIuQeSSHdXu/JCwg7JR5idqT1wBoOocCOvHJpr2EhQRgtehyxKloFRotPd188808/PDDDB48mOTkZEzTJDs7m/Hjx3PnnXeerxiF8Iqc4lyWbFuKzXCUmyYnT6DMVkZyZFcSwxOoyvkYTMP1+LJO/Xli7XHsxjGsFp2pVybLEaeiVWg0Uei6zmOPPcbtt9/Or7/+iq7r9OzZk+jo6PMVnxBes7soG7txstxUZitjVOcrXNedx5o67bdHupWbyuSIU9FKNJoo8vPziYuLIz4+nvj4eLdrX3/9NcOGDfNqcEJ4U3JkVyy6BdO0o2uWU442de8AqxHXFiy6ht1Q6Lom5SbRajQ6R1G7vHTXXXe5XZOzKERLoGpGDKrWyMFJC24DmgXQwBKArX2S61GnPlqIlqvRRKHUyX8OeXl5DV4TojnaXZSNaZqAox2Hc6UTOHZhV21c7thgp+kEDZrGLyURmGZNYjGVrHQSrUajiaJ2m/G6LcelBblo7pylJ+CU0lPtnk6gUJWlpFwUiUV3/NxL6Um0Jmc8ohCiJaqv9FTfsljnQURSehKtUaOJwjRNiouLOX78OIZhuD523haiOWuo9FS3p5M1ZSiWmCR27SuS0pNolRpd9ZSZmcmAAQNcI4v+/fu7rknpSTQXtXs4OduFQ03zP4sVu2F3a/7nWBarAyZYAgjsNhiAsJAAdE3DRMkmO9GqNJooMjIyzlccQnhFfT2cnMkiMTyBhy6/mx/27HAlEfdJbAtBg6ZhiUki60AxKz7fjWE6lsZOvVLOnxCtR6Olp3O1Zs0axowZw8iRI3nrrbcafNxXX33FFVdc0eB1Ic5WQz2cnLp1SGRU5yvqPZjIOYkNsGtfEXbDrLlbzp8QrUujI4pzUVBQwKJFi/jggw8IDAxkypQp9O/fn6Qk90Pnjxw5wlNPPeWtMEQrU7fM5DxbwjDdy0v1aWwSW8pOojXz2ohi48aNDBgwgIiICEJDQxk1ahRr16495XHz58+v98hVIZrKWWZak7OOxVuXklOcS2J4ArPTb2Nc4ii3slNdRkEWVZtX1ertdHISu3bZSdOk7CRaH6+NKA4fPkxUVJTrdnR0NNu3b3d7zBtvvMHFF19Mr169vBWGaEXqKzMlhie4/jTEdeaEq+SkuU1iS9lJtHZeSxSmabqtjFJKud3OzMxk/fr1vPbaaxw6dOis3qN9+zbnHGdtUVFtPfp63iJxnpR5JIdfD2fSI7obl3VJY23uF9hNA6tu4bIuaUR1OH0MQcV7KHeekY1GcJeetBt2PcGdUgCIjWrrKjtZrToDesb75Hsg33fPkjjPnNcSRWxsLJs3b3bdLiwsdOs6u3btWgoLC/mv//ovbDYbhw8fZtq0aSxfvvyM3+Po0VLXuvZzFRXVlsLCEo+8ljdJnCfVt6Lprt4njzCNVFGnjSEqqi3lRgCg4RxJ6D3HUxIUR0lhCVkHilm6aodrtdOU3yXTPizgvH8P5PvuWa01Tl3XzuoXbK/NUQwaNIhNmzZx7NgxKioqWL9+vVu32dmzZ7Nu3To++ugjli5dSnR0dJOShBANlZpqr2I6ncr9u07p6WSJObngQspOQngxUcTExDBnzhymT5/OpEmTGDduHD179mTmzJns2LHDW28rWhHniqbap9I1VcmOr+pdDuuUclGknGQnWj1NNeOGTlJ68l/nK85vD3zPtsPb6R3dkyHx/U//hFock9gLwaiZn9CthI6fxx57FLv2FblOrss6UOx22xfk++5ZrTXOsy09eW2OQghvyynOZeXu1dhNO1nFe4lrE3vGJSeo6elU0+vJuRx2jz2KZ1ZsxW6YWC06c6emkxQfLsthRavm1Z3ZQnjT6XZdn47jYKKTk9iB3Qa75iScx51K4z8hJFGIZiqnOJdjlUVYNMtZzVG4ejqZptsktnMHtiZzEkK4SOlJNDu1l8Xqms6guP7079i3SWWn+no6SeM/IeonIwrR7NQuOSll0i44oklJoqGeTrIUVoj6SaIQzU5yZFcsWv1HmJ4JxyT2yYO3nJPYR4srseiaLIUVog4pPYlmqb4jTM+U42Cik887Zj250knXNYb1imNQWkcpOwlRQ0YUotnZXZSNqU49wvRMuW+q0zh6+KhrpZMyFe3DgyVJCFGLjChEs1D7nImmnDFRH8eyWAsoE80aQFW7JHStUs6aEKIBkiiE36uv+d/s9NvqPQf7dOoedWrrcz0vf14lK52EaIQkCuH36ttY15TGf7XVXRZbcPAwdiOm5qasdBKiPpIohF/yZKnJqb5lsUZ0N3TthJSdhGiEJArhdzxZaqrNnp/hKDkBoFHWqT9LviqRspMQpyGJQvgdT5aaarPGpVKtWUDZQbeQaU3Fbq8pNUnZSYgGyfJY4XM5xbms2/slOcW5gGfOmTgTIUFWNOnrJMRpyYhC+FR9ZabE8ASPlJrqsmVugJqzsZVpkrP1R0zzEjQpOwnRKEkUwqcaOs7U+cdT6k5kK00jszoGBWhSdhKiUVJ6Ej51PspMRkEWVZtX1ervpFFx4QD2EyN9nYQ4AzKiEF6ReSSHH/buOG3pyFtlJifHcadP19o74TikKCp9BFNjQ9iRc4y0xHZSdhKiEZIohMflFOeyZNtSbIb7vENDPF1mqs3RKdZZVtKwxPcgqN8k9tijWPH5VgzD5Jeco3SKaiPJQogGSOlJeNzuomzsxtkfUepJjk6xOs6RRFC/SVhiklxnT5hy5KkQpyWJQnhccmRXLPrZnxfhKe59nU4edwqQclEkFl1DA3RdkzkKIRohiUJ4xbmcF+Ep9R13Wpuq87cQon6SKITH7S7KxjTP/rwIT2jouFOnXfuKME1HGlOmktKTEI2QRCE8Kqc4l2OVRVh0i9d3Vjemdl8nhUZ+eG/22KNc11MuisRq0WV5rBBnQFY9CY+pvcvaousMiutP/459vbaiqTHOvk5K2bErjXdzo9ifu5W5U9NJig8nKT6cuVPT2X+0nE7tQ2XFkxCNkEQhPKb2LmtTKdoFR/gkSdRHcXJ1kzMpJMWHM7B3JwoLS3wbnBB+TkpPwmPCAsIcTfbQsOq+W+0EUJCxDWUaaIAFk+SAQ1JiEuIsyYhCeEROcS4rd6/GVCa6pvOH9N+TeIFvRhNZB4r5ettRJgc7Jqs1DZK7xnNperqUmIQ4C5IohEc4y04AKEVJVZnPYtm1r4gQKlGArjnKTmnxwQRJkhDirEjpSXhEcmRXLNrJTXY9orv5LJawkADKzCA0QNVsknDs0BZCnA1JFMJj/GGTXdaBYlZ8vptQrQoTR9lJQztls50Q4sxJohAesbsoG1Od3GT36+FMn8Th7OGUZY/FRHekLN3ittlOCNE0kijEWTnd8aW+Kj05ezgJITzHq5PZa9as4Z///Cd2u52bb76ZG264we36559/zpIlS1BK0alTJ5588knCw2XC0d+dyfGl3Tok+mx/wkWWw4wM3IYFEw1AmdjzM1wNAYUQTeO1EUVBQQGLFi1i+fLlrFq1infeeYesrCzX9dLSUh555BGWLl3K6tWrSUlJYcmSJd4KR3hQfceXguNciVGdr/DpJrv8ndv5c9h6ugUcdExmo4FuldKTEOfAa4li48aNDBgwgIiICEJDQxk1ahRr1651XbfZbDz88MPExMQAkJKSwsGDB70VjvCg2hvrfNXLqT5ZB4oJPJqFBQOLBiZQ3SGF0HH3yGhCiHPgtdLT4cOHiYo62YQtOjqa7du3u25HRkZy1VVXAVBZWcnSpUu56aabmvQe7dt7dsljVFRbj76et/gyzswjObyftRpVs7Huj31+T/+ul9T72PMVZ+X+Xezb9iPvbazCboSS3NaCholutdJl7HSCO6U0+nz5vnuWxOlZ/hCn1xKFaZpo2slJRaWU222nkpIS7rzzTlJTU7nmmmua9B5Hj5Zimp5ZihkV1bZZ9PzxdZw/7N2BzbA72nMrxaFjxyi84NR4zleczjOxLYaN20J1/lEykhdKRjIxuZoeAwZSEhRHSSNx+PrreaYkTs9qrXHqunZWv2B7rfQUGxtLYWGh63ZhYSHR0dFujzl8+DDTpk0jJSWFBQsWeCsU4UF1Vzf5uuzkPJxIQ7l6Ou0nhtB+E6TcJISHeG1EMWjQIJYsWcKxY8cICQlh/fr1PPbYY67rhmFw++23c/XVV3PHHXd4KwzhBf1j+wCaz1qIO+X+so3wnV87T8RGt1iI79GHud17Sk8nITzIa4kiJiaGOXPmMH36dGw2G5MnT6Znz57MnDmT2bNnc+jQIX777TcMw2DdunUAXHLJJTKy8GN1l8X279jXZ7FkHShmy5dfMzrIQKvp5xSQMpRhQ4f6LCYhWiqv7qMYP34848ePd7tv2bJlAKSlpZGRkeHNtxceVt+yWF+NKHbtK6LECDzZz0kDSwf/OPtCiJZGdmaLM+ZPy2LDQgJoo1e7+jkh/ZyE8BpJFOKM1D5vQtM0JidP8NloIutAMRv/s4FwrbSmn5OGZgmQTXVCeImcRyHOSN3zJspsvjtvIn/ndv4Uug4LBiY6ByP7kjRstKxyEsJLJFGIM+IsO6Hwedkpxb4TKwZ6zQRF2+hYSRJCeJGUnsRp+VPZySjIIiTve9cktomGrb0kCSG8SUYU4rT8qexkz88AZaJpYCr4vjoJsyQCWe8khPfIiEKclr+sdso6UMyOA5UoTcNUYMfCVnsSKRdF+iQeIVoLSRSiUf5Sdso6UMy7766jy4FPUaYJus6e+Ku57rpRsgtbCC+T0pNolK/LTkZBFvb8DPKPhtNFP3iyhbhSpMUHEyRJQgivk0QhGuXL1U7OzrDKsJGmWdit+mFgAWWiW+QwIiHOF0kUokG1y066pp/XspNRkEXV5lUow4aGQjMNwvRqNsVOo09EETGpvWVJrBDniSQK0SBflZ2cIwmMasCxuslAZ3d1DH2iuxI3sPN5iUMI4SCJQpwipziX3UXZhAWEYdWtGKb9vJWdsg4UU755E50NG45jrjR22zvyaUUv9hPDVFnhJMR5J4lCuKnbSnxy8gTKbGUkR3b1etnJubIp3ZpHp0ANq6ahWaxEDbqOPiURTL0oUlY4CeEDkiiEm7qtxMtsZYzqfMV5ee9Tezj1IWnYaNrGJMmGOiF8SPZRCDfePurUKMiiauvHGAVZp1xLCihwLX/VkR5OQvgLGVGIU3jrqFPXJLVpo1oPIHTcPVhiksg6UMyufUVc0j4J3RKAadrRLVZiUnt77L2FEGdPEoVw8fZRp/b8DDBtNd387NjzM9hjj+KZFVuxGyarLTr3j76TWNt+rHGpMpoQwk9I6Um41HfUqSdpwW1w/MhpoDs2zO3aV4TdMFEKDMPkl5IIgtLHSZIQwo/IiEK4eHMXtlGQRdXG5aAM0CwEDZqGJSaJFHsxFl3Dbih0XZMGf0L4IRlRCMD7zf/s+Rlg2Bw3lOl2vrWq87cQwr9IohCA93dhO8pOJ1OC4zbs2leEaTruV6Zi174ij76vEOLcSempFXPuwE6O7OpaFuutXdi1RxCgceTwEbYe30tYSABWi45hmFgsupSehPBDkihaqbornGan38bs9NtciaMpZSdnK/DGVipZ41KptgSCaUdpFl77ySS7OgerRWfqlcmUVdhIkZ3XQvglSRStVH0rnEZ1vqLJ8xIN7Y2oyxKTROi4e7DnZ/D90XCyt9hcK53KKmyMlUZ/QvgtmaNo5nKKc1m390tyinOb9DxP7cC2ZW5wdHmttTeirqwDxXyyaS977FEEpY8jrntPrBYdXUPKTUI0AzKiaMbqKx+d6YggMTzhrEtNTkZBFrZd35y8Q9NPOUwo60Cxa0Od1aIzd2o6SfHhzJ2azq59RVJuEqIZkETRjNVXPmrKf/iJ4QnntATWsdPacN22pgw9pexUd0Pdrn1FJMWHu/4IIfyflJ78XGOlJW838KvNWT7KOlDsus99yStYOpyadFIuipQykxDNnIwo/Fh9paWoqEtc1z1RPjoTDZWP6i55db/tIGUmIZo/SRR+rL7SUn8ucXvMuZaPzkTt8lEnCijfvBrDOtBtyauzd1N9pMwkRPMmicKHam94q+8/e29vgnNytvlu6Dd+Z/moEwXc0XY9AQUm5R9/Q+i4e1xLXqXbqxAtV4tLFGey+csfnMmKpfNRWmqorFSbs3xUvnk1AQUmGieXwkqnVyFaPq9OZq9Zs4YxY8YwcuRI3nrrrVOu79y5k2uvvZZRo0bxwAMPYLfbz+n9nJu/qje/T/nHT9d7ipq/ONOW3onhCWe1Ee5M1bcqqT5J8eH0GDAQzRIAmt5oqUkI0bJ4LVEUFBSwaNEili9fzqpVq3jnnXfIynL/j3vu3Lk89NBDrFu3DqUU77777jm9Z30H4/ir87liqTFNWZXk3F0d2O/aBndgCyFaHq8lio0bNzJgwAAiIiIIDQ1l1KhRrF271nX9wIEDVFZW0ru347jLa6+91u362bDGpYLePH7jdZaVxiWOatJGOU9zlpWuGZZYb9mpLktMkpSbhGhlvDZHcfjwYaKioly3o6Oj2b59e4PXo6KiKCgoOKf3rN1PyN/nKOD8rFg6E7IqSQjRGK8lCtN0HIDjpJRyu32662eiffs2p94ZlQ6XpDc9YCAqqu1ZPe98kzg9S+L0LInTs/whTq+VnmJjYyksLHTdLiwsJDo6usHrR44ccbsuhBDCP3gtUQwaNIhNmzZx7NgxKioqWL9+PcOGDXNdj4+PJygoiC1btgDw0UcfuV0XQgjhHzSllNeOKl6zZg0vvfQSNpuNyZMnM3PmTGbOnMns2bNJS0sjIyOD+fPnU1paSo8ePXjyyScJDAz0VjhCCCHOglcThRBCiOZPuscKIYRolCQKIYQQjZJEIYQQolGSKIQQQjRKEoUQQohGSaIQQgjRqFabKEpLSxk3bhz79+8HHE0Mx48fz8iRI1m0aJGPo3N4/vnnGTt2LGPHjuXpp58G/DPO5557jjFjxjB27FheffVVwD/jdHrqqaeYN28e4PlW955w0003MXbsWCZOnMjEiRP5+eefT9uy3xe+/PJLrr32Wq6++moef/xxwP++7++9957r6zhx4kT69u3Lo48+6ndxgmPTsfPf+1NPPQX40c+naoW2bdumxo0bp3r06KHy8vJURUWFGj58uNq3b5+y2WxqxowZ6quvvvJpjBs2bFDXX3+9qqqqUtXV1Wr69OlqzZo1fhfn999/r6ZMmaJsNpuqqKhQI0aMUDt37vS7OJ02btyo+vfvr+69916llFJjx45VW7duVUopdd9996m33nrLl+Ep0zTVkCFDlM1mc9136NAhNWLECFVUVKTKysrU+PHj1e7du30YpVL79u1TQ4YMUQcPHlTV1dVq6tSp6quvvvLb77tSSmVmZqqrrrpK5efn+12c5eXl6tJLL1VHjx5VNptNTZ48WW3YsMFvfj5b5Yji3Xff5eGHH3b1ltq+fTsJCQlceOGFWK1Wxo8ff84tz89VVFQU8+bNIzAwkICAALp27crevXv9Ls7LLruMN954A6vVytGjRzEMgxMnTvhdnADHjx9n0aJF3H777YB3Wt2fq5ycHABmzJjBhAkTePPNN0/bst8XPvvsM8aMGUNsbCwBAQEsWrSIkJAQv/y+Oz3yyCPMmTOHvLw8v4vTMAxM06SiogK73Y7dbsdqtfrNz2erTBQLFiygX79+rtv1tUQ/15bn5yo5Odn1A7J3714+/fRTNE3zuzgBAgICWLx4MWPHjmXgwIF++fUEeOihh5gzZw4XXHAB4J1W9+fqxIkTDBw4kH/84x+89tprvP322+Tn5/vd1zM3NxfDMLj99tuZOHEiy5cv99vvOzhKYpWVlVx99dV+GWebNm347//+b66++mqGDx9OfHw8AQEBfvPz2SoTRV2eaHnuLbt372bGjBncc889XHjhhX4b5+zZs9m0aRMHDx5k7969fhfne++9R8eOHRk4cKDrPn/8vqenp/P000/Ttm1b2rVrx+TJk1m8eLHfxWkYBps2beKJJ57gnXfeYfv27eTl5fldnE5vv/02f/zjHwH//L5nZGTw/vvv85///IdvvvkGXdfZsGGD38TptfMompPTtUT3lS1btjB79mzuv/9+xo4dyw8//OB3cWZnZ1NdXU337t0JCQlh5MiRrF27FovF4nqMP8T5v//7vxQWFjJx4kSKi4spLy9H0zS/a3W/efNmbDabK6EppYiPj/e773uHDh0YOHAg7dq1A+DKK6/0y+87QHV1NT/++CMLFy4E/PPf+7fffsvAgQNp37494CgzvfLKK37z8ykjCqBXr17s2bPHNZz++OOPfd7y/ODBg9x55508++yzjB071m/j3L9/P/Pnz6e6uprq6mq++OILpkyZ4ndxvvrqq3z88cd89NFHzJ49myuuuIInn3zS71rdl5SU8PTTT1NVVUVpaSkffvghzzzzTKMt+31hxIgRfPvtt5w4cQLDMPjmm28YPXq0333fAXbt2kXnzp0JDQ0F/PPfUWpqKhs3bqS8vBylFF9++SWXXXaZ3/x8yogCCAoKYuHChdx1111UVVUxfPhwRo8e7dOYXnnlFaqqqly/BQFMmTLF7+IcPnw427dvZ9KkSVgsFkaOHMnYsWNp166dX8XZkGeffdat1f306dN9Gs+IESP4+eefmTRpEqZpMm3aNPr27cucOXOYPn26q2V/z549fRpnr169uPXWW5k2bRo2m43BgwczdepUEhMT/e77npeXR2xsrOu2P/57HzJkCL/99hvXXnstAQEBpKWlcdttt3HVVVf5xc+ntBkXQgjRKCk9CSGEaJQkCiGEEI2SRCGEEKJRkiiEEEI0ShKFEEKIRkmiEGdl//79dO/e3a0z54QJE1i5cqWvQ2PGjBkcO3asSc/59ttvGTFiBJMnT6aystJ1/3333cdDDz10yuPXrVvHhAkTGn3NvLw87rrrribFAfDBBx9w+eWXc8sttzT5ubUdO3aM+fPnc9VVVzFhwgQmTZrEyy+/jGEYAHz//feMGzfunN5DtA6SKMRZCw4O5qOPPnL9WbZsGU899RQZGRk+jWvDhg1Nfs4nn3zC73//e1auXElwcLDr/mnTpvHJJ5+4JQ9wNJa84YYbGn3N/Px89uzZ0+RYVq1axZw5c3jllVea/FynEydOMHXqVDp37synn37K6tWref3119mxYwf33HPPWb+uaJ1kw53wmJiYGBISEti7dy+pqam89957rFixAtM0iYiI4MEHH6Rr167MmzeP48ePk5eXx+WXX84dd9zB448/zk8//YTFYuHKK69kzpw52Gw2nn32WX788UcMw+Diiy9m/vz5tGnThiuuuIJrrrnG1V9q4sSJ3H333dx3330A3HzzzSxdupSOHTu64rPZbCxcuJBNmzZhsVjo2bMn9913H2+//TZffPEFQUFBlJSUcO+997qek5aWRpcuXVi7di2TJk0CHKOpX375heeffx6Azz//nOeffx7TNAkLC+O+++6jR48ezJ8/n4KCAm655RZeeeUVfvrpJ5599lkqKirQdZ1Zs2YxYsQIt6/hE088wY4dO9i/fz9FRUX813/9F3/961/JyMhA0zSGDh3KX/7yF6xWK5dccgm/+93vyMjI4NlnnyUtLc31OitWrKB79+7ceuutrvvCw8N5+umnGTFiBNu3bwegvLyc2bNnk5ubywUXXMCjjz5Kly5d2LNnD48++ihlZWUUFhaSmprK//zP/xAUFERaWhp//OMfXTuJZ82axdq1a8nMzCQ6OpoXX3yR0NBQVq5cyTvvvIPNZqO4uJiZM2cybdo0D//UifPCJ83NRbOXl5enevfu7XbfTz/9pC699FKVn5+vvv/+ezVt2jRVXl6ulFLqm2++UaNHj1ZKKXXvvfeqm2++2fW8J554Qs2ZM0fZ7XZVVVWlbrjhBvXdd9+pJUuWqIULFyrTNJVSSv3tb39TDz/8sFJKqWSsTWYAAAXeSURBVBEjRqiFCxcqpRznNaSlpal9+/YppZTq1q2bOnr06CkxP/fcc2rWrFmqurpaGYah5s2bpx588EFXTC+//HK9n+v777+vbrzxRtftv//972rBggVKKaWysrLUoEGDXO+9ceNGNXjwYFVSUqK+++47NXbsWKWUUsePH1cjR45UeXl5rpiHDRumDhw4cMr73XjjjerTTz9VSil1zz33qMcee0yZpqmqqqrUjBkz1EsvveT6PD/88MN6Y/7Tn/6k3nzzzXqvzZo1S7366qvqu+++U6mpqWrLli1KKaXefvttNXnyZKWUUgsXLlSrVq1SSilVXV2txo0bp9auXet639dff10ppdRLL72k0tPT1aFDh5RhGOqaa65Rq1evVqWlpeq6665Tx44dU0optXXr1lN+XkTzISMKcdYqKyuZOHEi4OgmGhkZyTPPPEPHjh3597//TW5uLlOmTHE9/sSJExw/fhyAvn37uu7fuHEj9913HxaLBYvFwptvvgnAM888Q0lJCRs3bgQcIwJn0zSA3/3ud4BjJNO+fXuKi4u58MILG4z366+/Zs6cOQQEBACOk+TuvPPO036ezhMG9+3bR1xcHB9++CFvvPEGAN999x0DBgxwva+zUd4vv/zi1ulz27ZtFBYWur2fpmns2rWLuLi4RmNesWIFmqYRGBjIlClTeP3117ntttsA3Nrl12Wz2eq9v7q62vVxSkoKffr0AeCaa67hkUceoaSkhLlz57JhwwaWLVvG3r17OXz4MOXl5a7njRo1CoCLLrqIbt26ERMTA0CnTp0oLi4mLCyMF198kf/7v/9j7969ZGRkuD1fNC+SKMRZc85R1Mc0TSZOnMjcuXNdtw8fPkx4eDiAq0EbgNVqdftP9eDBgwQHB2OaJvfffz/Dhw8HoKysjKqqKtfjgoKCXB9rmoY6TTeauu2lTdNs8D/T2oKCgrjmmmt4//33SUtLIzk5mc6dO9f7muDo+Gq3210JCRyJtGvXrrz33nuu+woKClzdV5sSc+3jMGt/HWvr06cPP/zwA3/4wx/c7i8rK2PHjh3ceeedrhJYbZqmYbVa+ctf/oJhGFx99dVcfvnlHDx40O3rW/tzq/2x06FDh7j++uu57rrr6Nu3L6NHj+Y///lPo5+r8F8ymS28YsiQIXzyySccPnwYcNTMb7755nofO3DgQD788ENM06S6uprZs2fz448/MmTIEN566y2qq6sxTZMHH3yQv//976d9b4vFUu/ZwkOHDmXFihXYbDZM0+Stt95i8ODBZ/T5OCe1P/jgA2688Ua32L/99lvy8vIAXHMmvXr1wmKxuBJR7969yc3N5ccffwQcZyGPGjXqtAfRDBkyhDfffBOlFNXV1bz77rsMGjTojOLNzs5m6dKlrlVOxcXFzJs3j379+rmaCu7atYudO3cC8M4779C3b19CQkL49ttvufPOOxkzZgwAP//8s+t1zsQvv/xCu3btuOOOOxgyZIgrSTTlNYT/kBGF8IohQ4Ywc+ZMZsyYgaZptGnThueff77eg1dmzZrFggULmDhxIoZhMGbMGEaOHMmwYcN46qmnuOaaazAMg+7duzNv3rzTvvfo0aO56aabWLJkCd26dXPd/+c//5mnnnqKSZMmYbfb6dmzJw8++OAZfT4XXnghiYmJZGZmukY4AElJSTz88MP/f3t3iOsgEEZR+CIaSAOmWBRhC60heNKAYwVYMHhkVV0bBFsgsClgGYTwHHJS+cT59GQmGXOSEf+ormvt+y7HcdT3vTzPUxRFsm1bRVFoHEd9v99zhPhxHHq/3wqCwHhu27Z6vV7K81zbtilJkvMrVxPXdTUMgz6fj57Ppy6XiyzLUpZlKsvyXBeGobqu07qu8n3/nFbcNI2qqtL1epXrurrf71qW5ae7kqQ4jjVNk9I0lWVZejweut1umudZYRj+vA/+B6bHAgCMeHoCABgRCgCAEaEAABgRCgCAEaEAABgRCgCAEaEAABgRCgCA0R8vsSTg2uIxaAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_PA = np.sort(swing_state[swing_state['state'] =='PA']['dem_share'])\n",
    "x_OH = np.sort(swing_state[swing_state['state'] =='OH']['dem_share'])\n",
    "x_FL = np.sort(swing_state[swing_state['state'] =='FL']['dem_share'])\n",
    "\n",
    "y_PA = np.arange(1, len(x_PA)+1)/len(x_PA)\n",
    "y_OH = np.arange(1, len(x_OH)+1)/len(x_OH)\n",
    "y_FL = np.arange(1, len(x_FL)+1)/len(x_FL)\n",
    "\n",
    "_ = plt.plot(x_PA,y_PA, marker ='.', linestyle='none')\n",
    "_ = plt.plot(x_OH,y_OH, marker ='.', linestyle='none')\n",
    "_ = plt.plot(x_FL,y_FL, marker ='.', linestyle='none')\n",
    "plt.xlabel('Percent of Vote for Obama')\n",
    "plt.ylabel('ECDF')\n",
    "plt.legend(['Pennslvanie', 'Ohio','Florida'])\n",
    "#Keep the data off from plot edge\n",
    "plt.margins(0.02) \n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Quantitative Exploratory Data Analysis\n",
    "**Mean**: If you have a sample of n values,  $x_i$, the mean, $\\mu$, is the sum of the values divided by the number of values:\n",
    "\\begin{equation}\n",
    "\\mu = \\sum \\frac{1}{n} x_i \n",
    "\\end{equation}\n",
    "**Outliers:** Data point whose value is far greater or less than most of the rest of the data.\n",
    "* The mean highly effected from outliers <br>\n",
    "**The median:** is the middle value of the dataset and is immune to data that have extreme values.The median is the special name for the 50th percentile.\n",
    "Similiarly, the 25th percentile is the value of the data point that is greater than 25% of the sorted data.\n",
    "```python\n",
    "np.percentile(data, [25, 50, 75])\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean:  43.76441441441444\n",
      "Median:  43.185\n"
     ]
    }
   ],
   "source": [
    "print('Mean: ', np.mean(swing_state['dem_share']))\n",
    "print('Median: ',np.median(swing_state['dem_share']))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([37.3025, 43.185 , 49.925 ])"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.percentile(swing_state['dem_share'], [25,50,75])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Box Plot\n",
    "Box plot were invented by John Tukey to display some of the statistical features of the data set based on percentiles."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = sns.boxplot(x ='state', y= 'dem_share', data=swing_state)\n",
    "_ = plt.title('Percent of Vote for Obama for different states')\n",
    "_ = plt.xlabel('State')\n",
    "_ = plt.ylabel('Percent of Vote for Obama')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here we look at the box plot for percent of Vote for Obama for different states.\n",
    "* The center of boxes are shown the median: 50th\n",
    "* The edges of the boxes are shown the 25th and 75th percentile\n",
    "* The total height of the box contains the 50% of the data and it is called interquartile range or **IQR**\n",
    "* The whiskers extend the distance of 1.5 times IQR ot to the extent a distance of the data.\n",
    "* All points outside of the whiskers are called outliers."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[25.58675 37.3025  43.185   49.925   64.7195 ]\n",
      "[0.02939189 0.25337838 0.50225225 0.75112613 0.97511261]\n"
     ]
    }
   ],
   "source": [
    "percentiles = np.array([2.5, 25, 50, 75, 97.5])\n",
    "per_vers_x = np.percentile(x, percentiles)\n",
    "per_vers_y = np.percentile(y, percentiles)\n",
    "print(per_vers_x)\n",
    "print(per_vers_y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 66,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.sort(swing_state['dem_share'])\n",
    "y = np.arange(1, len(x) +1) /len(x)\n",
    "percentiles = np.array([2.5, 25, 50, 75, 97.5])\n",
    "\n",
    "_ = plt.plot(x,y, marker ='.', linestyle='none')\n",
    "plt.xlabel('percent of vote for Obama')\n",
    "plt.ylabel('ECDF')\n",
    "\n",
    "_ = plt.plot(per_vers_x, percentiles/100, marker='D', color='red', linestyle ='none')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Variance and standard deviation\n",
    "**Variance:** is intended to describe the spread of the data.\n",
    "The variance is calculated as the average of the squared distance from mean. in python with numpy we can calculate the variance *nump.var()*\n",
    "\\begin{equation}\n",
    "\\sigma^2 = \\frac{1}{n} \\sum (x_i - \\mu)^2\n",
    "\\end{equation}\n",
    "$x_i - \\mu$ is called deviation from mean so variance is the mean squared deviation. The square root of the variance, $\\sigma$, is called the **standart deviation.** Standart deviation is resonable metric for the spread of the data and calculated with *numpy.std()* \n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Variance:  114.24649492735986\n",
      "Standart deviation:  10.68861520157592\n",
      "Standart deviation is squared root of variance, 10.68861520157592\n"
     ]
    }
   ],
   "source": [
    "print('Variance: ', np.var(swing_state['dem_share']))\n",
    "print('Standart deviation: ', np.std(swing_state['dem_share']))\n",
    "print('Standart deviation is squared root of variance,' , np.sqrt(np.var(swing_state['dem_share'])))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Covariance, and Pearson Correlation Coefficient\n",
    "**Covariance** is a measure of the tendency of two variables to vary together.\n",
    "If we have two series, X and Y, their deviations from the mean are\n",
    "\\begin{equation}\n",
    "dx_i = x_i -  \\mu_X \\\\\n",
    "dy_i = y_i - \\mu_Y\n",
    "\\end{equation}\n",
    "where $\\mu_X$ is the mean of X and $\\mu_Y$ is the mean of Y. If X and Y vary together,\n",
    "their deviations tend to have the same sign.\n",
    "\n",
    "If we multiply them together, the product is *positive* when the deviations have the same sign and *negative* when they have the opposite sign. So adding up the products gives a measure of the tendency to vary together.\n",
    "\n",
    "*Covariance is the mean of these products:*\n",
    "\n",
    "\\begin{equation}\n",
    "Cov(X,Y) = \\frac{1}{n} \\sum dx_i dy_i\n",
    "\\end{equation}\n",
    "where n is the length of the two series (they have to be the same length).\n",
    "\n",
    "We are going to make scatter plot for the percent of votes for Obama versus total number of votes in each county."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 161,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "43.76441441441444\n",
      "90.42451351351352\n"
     ]
    }
   ],
   "source": [
    "mean_of_dem_share = np.mean(swing_state['dem_share'])\n",
    "mean_of_total_vote =np.mean(swing_state['total_votes'])/1000\n",
    "\n",
    "_ = plt.plot(swing_state['total_votes']/1000, swing_state['dem_share'], marker='.',\n",
    "            linestyle='none')\n",
    "#drawing the mean of total votes\n",
    "_ = plt.axvline(x=mean_of_total_vote, ymin=0, ymax= max(swing_state['total_votes']),\n",
    "                color='red', zorder=1, alpha=0.8 )\n",
    "_ = plt.text(480,45,'Mean of percent for Obama', color='r')\n",
    "#draw tha mean of percent of votes for Obama\n",
    "_ = plt.axhline(y=mean_of_dem_share, xmin=0, xmax= max(swing_state['dem_share']),\n",
    "                color='red', zorder=1, alpha=0.8)\n",
    "_ = plt.text(100, 10, 'Mean of total votes', color='r')\n",
    "\n",
    "#distance from mean\n",
    "_ = plt.vlines(x=220, ymin=44, ymax=65., color='g')\n",
    "_ = plt.hlines(y=65, xmin=85, xmax=220, color='b')\n",
    "\n",
    "_ = plt.text(100, 70, 'distance from mean of total votes', color='b')\n",
    "_ = plt.text(205,60,'distance from mean of percent for Obama', color='g')\n",
    "#_ =plt.axline()\n",
    "#data point\n",
    "\n",
    "_ = plt.xlabel('Total Votes (thousands)')\n",
    "_ = plt.ylabel('Percent of Votes for Obama ')\n",
    "\n",
    "\n",
    "plt.show()\n",
    "print(mean_of_dem_share)\n",
    "print(mean_of_total_vote)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* 12 of the counties with highes population is voted for Obama\n",
    "* Most of the counties with small population is not voted for Obama\n",
    "\n",
    "*if you look at the data point we point out*\n",
    "Covariance is the mean of the product of diffences which is calculates using distance from mean of percent for Obama and distance from mean of toral votes.\n",
    "\n",
    "**Postively Correlated:** If x and y both tend to be above, or both below their respective means together then covariance is positive\n",
    "\n",
    "**Nagatively Correlated:** If x is high while y is low then covariance is negative or anticorrelated. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If we want to have a more generaly applicable measure of how two varibales depend on each other, we want to be dimensionless. We can divide the covarince by standar deviation ($\\sigma$) of x and y varianles.\n",
    "\n",
    "**Pearson’s correlation ( $\\rho$ ):** Pearson’s correlation is always between $-1$ and $+1$ (including both). The magnitude indicates the strength of the correlation. If $r = 1$ the variables are perfectly correlated, which means that if you know one, you can make a perfect prediction about the other. The same is true if $r = -1$. It means that the variables are negatively correlated, but for purposes of prediction, a negative correlation is just as good as a positive one. So if $r = 0$, does that mean there is no relationship between the variables? Unfortunately, no. Pearson’s correlation only measures linear relationships.\n",
    "\n",
    "\\begin{equation}\n",
    "\\rho = \\frac{Cov(x,y)}{\\sigma_x \\sigma_y}\n",
    "\\end{equation}"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The covariance may be computed using the Numpy function `np.cov()`. For example, we have two sets of data x and y, `np.cov(x, y) returns a 2D array` where entries [0,1] and [1,0] are the covariances. Entry [0,0] is the variance of the data in x, and entry [1,1] is the variance of the data in y. This 2D output array is called the covariance matrix, since it organizes the self- and covariance."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 171,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance matrix between percent of vote for Obama and total votes is\n",
      " [[1.14763447e+02 8.17309362e+05]\n",
      " [8.17309362e+05 2.02451039e+10]]\n"
     ]
    }
   ],
   "source": [
    "Covariance_matrix = np.cov(swing_state['dem_share'], swing_state['total_votes'])\n",
    "print('Covariance matrix between percent of vote for Obama and total votes is\\n', Covariance_matrix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 172,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1: Variance of X from np.var(): 114.24649492735986\n",
      "2: Variance of X from covariance matrix 114.76344739309454\n"
     ]
    }
   ],
   "source": [
    "# let's compare variance x from var and covariance matrix\n",
    "print('1: Variance of X from np.var():', np.var(swing_state['dem_share']))\n",
    "print('2: Variance of X from covariance matrix', Covariance_matrix[0,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 173,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1: Variance of y from np.var(): 20153909774.448013\n",
      "2: Variance of y from covariance matrix 20245103936.323345\n"
     ]
    }
   ],
   "source": [
    "# let's compare variance y from var and covariance matrix\n",
    "print('1: Variance of y from np.var():', np.var(swing_state['total_votes']))\n",
    "print('2: Variance of y from covariance matrix', Covariance_matrix[1,1])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 174,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Covariance matrix between percent of vote for Obama and total votes is\n",
      " 817309.3618405284\n"
     ]
    }
   ],
   "source": [
    "print('Covariance matrix between percent of vote for Obama and total votes is\\n',Covariance_matrix[1,0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 175,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.536197364958678\n"
     ]
    }
   ],
   "source": [
    "pearson_coefficient = np.corrcoef(swing_state['dem_share'], swing_state['total_votes'])\n",
    "print(pearson_coefficient[0,1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Probabilistic logic and statistical inference\n",
    "\n",
    "Given a set of data, you describe probablitically what you might expect if those data were acquired again and again. This is the heart of statistical inference.\n",
    "\n",
    "It is the process by which we go from measured data to probabilistic conclusions abaout waht we might expect if we collected the same data again.\n",
    "## Random number generators and hacker statistics\n",
    "\n",
    "We are going to think probabilistically using hacker statistics. The basic idea of hacker statistic is that instead of literally repating the data acquisition over and over again. We can simulate those repeated measurements using Python.\n",
    "\n",
    "**Bernoulli trail** is an experiment that has two options \"success\" (True) or \"failure\" (False)\n",
    "\n",
    "The pseudorandom number generator work by starting with an integer, called a seed, and then generates random number in succesion. the same seed gives the same the same sequence of random numbers hence the name pseudorandom number generation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 180,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of 10000 repeats of the 4 flips trail 0.063\n"
     ]
    }
   ],
   "source": [
    "#Let's look at the simulation of 4 coin flips\n",
    "n_all_heads = 0 \n",
    "for i in range(10000):\n",
    "    head = np.random.random(size=4) < 0.5\n",
    "    n_head =np.sum(head)\n",
    "    if (n_head==4):\n",
    "        n_all_heads +=1\n",
    "print('Probability of 10000 repeats ',n_all_heads/10000)   \n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Generating random numbers using the np.random module\n",
    "We will be hammering the np.random module for the rest of this course and its sequel. Actually, you will probably call functions from this module more than any other while wearing your hacker statistician hat. Let's start by taking its simplest function, np.random.random() for a test spin. The function returns a random number between zero and one. Call np.random.random() a few times in the IPython shell. You should see numbers jumping around between zero and one.\n",
    "\n",
    "In this exercise, we'll generate lots of random numbers between zero and one, and then plot a histogram of the results. If the numbers are truly random, all bars in the histogram should be of (close to) equal height.\n",
    "\n",
    "You may have noticed that, in the video, Justin generated 4 random numbers by passing the keyword argument size=4 to np.random.random(). Such an approach is more efficient than a for loop: in this exercise, however, you will write a for loop to experience hacker statistics as the practice of repeating an experiment over and over again.\n",
    "   "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 183,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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EAMAU4xPcAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMCIWAAAjYgEAMJpULH7961+rsLBQhYWFeuWVVyRJnZ2d8vl8ysvLU0NDQ3Tf7u5u+f1+eb1eVVVVKRQKSZIuXLigkpIS5efnq7y8XENDQ5NZEgBgCsQci87OTh05ckR79+5VS0uLTp06pf3792vTpk1qbGxUW1ubTp48qcOHD0uSKioqVFNTo/b2dlmWpebmZknS5s2bVVxcrEAgoEWLFqmxsTE+kwEA4ibmWDidTlVWVuqBBx6Qw+HQ5z73OZ05c0YLFizQ/PnzZbfb5fP5FAgEdP78eQ0PDysnJ0eS5Pf7FQgENDo6qqNHj8rr9Y7ZDgC4s9hjPfCRRx6J/vuZM2d04MABPfPMM3I6ndHtLpdLPT096u3tHbPd6XSqp6dH/f39Sk1Nld1uH7P9dsyZkxrrCABwV3M6Z0/buWKOxQ0ffPCBnnvuOb344otKTk7WmTNnovdZliWbzaZIJCKbzTZu+42vN7v1tsnly4OKRKyY1j6d32gAiLdgcOC2j0lKssX0JHtSb3B3dXXpO9/5jn784x9rxYoVysjIUDAYjN4fDAblcrnGbe/r65PL5VJ6eroGBgYUDofH7A8AuLPEHIuLFy/q+9//vurr61VYWChJWrx4sU6fPq2zZ88qHA5r//798ng8yszMVEpKirq6uiRJra2t8ng8cjgccrvdamtrkyS1tLTI4/HEYSwAQDzF/GuoV199VSMjI9q6dWt025o1a7R161atX79eIyMjys3NVX5+viSpvr5e1dXVGhwcVHZ2tkpLSyVJtbW1qqys1I4dOzRv3jxt27ZtkiMBAOIt5lhUV1erurr6P963b9++cduysrK0Z8+ecdszMzPV1NQU6zIAANOAT3ADAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDAiFgAAIyIBQDA6I6IxZtvvqlly5YpLy9Pu3fvTvRyAAC3sCd6AT09PWpoaNAbb7yhBx54QGvWrNFXv/pVPfzww4leGgDg/0l4LDo7O/W1r31NaWlpkiSv16tAIKAf/OAHEzo+Kck2qfO7Hpw5qeM5751/bma+P859v51Xiu3xL9bHTJtlWVZMR8bJb3/7W127dk0bN26UJL3++us6ceKEXnrppUQuCwBwk4S/ZxGJRGSz/f/SWZY15jYAIPESHouMjAwFg8Ho7WAwKJfLlcAVAQBulfBYfP3rX9fbb7+tK1eu6Pr16zp48KA8Hk+ilwUAuEnC3+CeO3euNm7cqNLSUo2OjmrVqlX6whe+kOhlAQBukvA3uAEAd76E/xoKAHDnIxYAACNiAQAwIhYAAKN7PhamixR2d3fL7/fL6/WqqqpKoVAoAauML9PMf/7zn/X0009r+fLlev755/XJJ58kYJXxNdGLUXZ0dOiJJ56YxpVNHdPMH374ob71rW9p+fLl+t73vndf/JxPnTqllStXavny5Xruued09erVBKwyvgYHB1VUVKSPP/543H3T+vhl3cMuXbpkLV261Orv77eGhoYsn89nffDBB2P2KSwstP7xj39YlmVZP/vZz6zdu3cnYqlxY5p5YGDAeuyxx6xLly5ZlmVZ27dvt1566aVELTcuJvJztizLCgaDVn5+vrV06dIErDK+TDNHIhErLy/POnz4sGVZlvXLX/7SeuWVVxK13LiYyM957dq1VkdHh2VZlrVlyxZr27ZtiVhq3Bw/ftwqKiqysrOzrXPnzo27fzofv+7pVxY3X6Rw1qxZ0YsU3nD+/HkNDw8rJydHkuT3+8fcfzcyzTw6Oqra2lrNnTtXkrRw4UJdvHgxUcuNC9PMN1RXV0/4ApV3OtPMp06d0qxZs6IfcF23bp1KSkoStdy4mMjPORKJaGhoSJJ0/fp1zZgxIxFLjZvm5mbV1tb+x6taTPfj1z0di97eXjmdzuhtl8ulnp6e//F+p9M55v67kWnmBx98UE899ZQkaXh4WLt27dKTTz457euMJ9PMkvSHP/xBn//857V48eLpXt6UMM380Ucf6aGHHtKmTZu0YsUK1dbWatasWYlYatxM5OdcWVmp6upqPf744+rs7NSaNWume5lxVVdXJ7fb/R/vm+7Hr3s6FqaLFN6LFzGc6EwDAwMqKytTVlaWVqxYMZ1LjDvTzO+//74OHjyo559/PhHLmxKmmUOhkN555x2tXbtWe/fu1fz587V169ZELDVuTDMPDw+rqqpKv//973XkyBEVFxfrpz/9aSKWOi2m+/Hrno6F6SKFt97f19d311/EcCIXZuzt7VVxcbEWLlyourq66V5i3JlmDgQCCgaDWrlypcrKyqLz381MMzudTi1YsECPPvqoJKmoqEgnTpyY9nXGk2nm999/XykpKdHLBX3zm9/UO++8M+3rnC7T/fh1T8fCdJHCzMxMpaSkqKurS5LU2tp611/E0DRzOBzWunXrVFBQoKqqqrv+lZRknvmFF15Qe3u7WltbtWvXLrlcLr322msJXPHkmWb+4he/qCtXrui9996TJB06dEjZ2dmJWm5cmGZesGCBLl26pA8//FCS9Je//CUay3vRtD9+Tdlb53eIffv2WYWFhVZeXp61a9cuy7Is69lnn7VOnDhhWZZldXd3WytXrrS8Xq/1ox/9yBoZGUnkcuPif5v54MGD1sKFC63ly5dH/9m0aVOCVzx5pp/zDefOnbsn/jaUZZlnPn78uLVy5Upr2bJl1ne/+12rr68vkcuNC9PMHR0dls/ns4qKiqxvf/vb1kcffZTI5cbN0qVLo38bKlGPX1xIEABgdE//GgoAEB/EAgBgRCwAAEbEAgBgRCwAAEbEAgBgRCwAAEbEAgBg9H8BRyU+S/ltHekAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "#Seed the random number generator using the seed 42\n",
    "np.random.seed(42)\n",
    "#Initialize an empty array\n",
    "random_numbers = np.empty(100000)\n",
    "#-Write a for loop to draw 100,000 random numbers using np.random.random()\n",
    "for i in range(100000):\n",
    "    random_numbers[i] = np.random.random()\n",
    "#Plot a histogram of random_numbers\n",
    "_ =plt.hist(random_numbers)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The np.random module and Bernoulli trials\n",
    "\n",
    "You can think of a Bernoulli trial as a flip of a possibly biased coin. Specifically, each coin flip has a probability p of landing heads (success) and probability 1−p of landing tails (failure). In this exercise, you will write a function to perform n Bernoulli trials, perform_bernoulli_trials(n, p), which returns the number of successes out of n Bernoulli trials, each of which has probability p of success. To perform each Bernoulli trial, use the np.random.random() function, which returns a random number between zero and one."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 185,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Define a function with signature perform_bernoulli_trials(n, p).\n",
    "def perform_bernoulli_trials(n, p):\n",
    "    \"\"\"Perform n Bernoulli trials with success probability p\n",
    "    and return number of successes.\"\"\"\n",
    "    # Initialize number of successes: n_success\n",
    "    n_success = 0\n",
    "    # Perform trials\n",
    "    for i in range(n):\n",
    "        # Choose random number between zero and one: random_number\n",
    "        random_number = np.random.random()\n",
    "        # If less than p, it's a success so add one to n_success\n",
    "        if random_number < p:\n",
    "            n_success += 1\n",
    "    return n_success    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### How many defaults might we expect?\n",
    "Let's say a bank made 100 mortgage loans. It is possible that anywhere between 0 and 100 of the loans will be defaulted upon. You would like to know the probability of getting a given number of defaults, given that the probability of a default is p = 0.05. To investigate this, you will do a simulation. You will perform 100 Bernoulli trials using the perform_bernoulli_trials() function you wrote in the previous exercise and record how many defaults we get. Here, a success is a default. (Remember that the word \"success\" just means that the Bernoulli trial evaluates to True, i.e., did the loan recipient default?) You will do this for another 100 Bernoulli trials. And again and again until we have tried it 1000 times. Then, you will plot a histogram describing the probability of the number of defaults."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 188,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Seed the random number generator to 42\n",
    "np.random.seed(42)\n",
    "#Initialize n_defaults with 1000 entries\n",
    "n_defaults = np.empty(1000)\n",
    "#Write a for loop with 1000 iterations to compute the number of defaults per \n",
    "#100 loans using the perform_bernoulli_trials() function\n",
    "for i in range(1000):\n",
    "    n_defaults[i] = perform_bernoulli_trials(100, 0.05)\n",
    "\n",
    "#print(n_defaults)\n",
    "_ = plt.hist(n_defaults, density=True) \n",
    "_ = plt.xlabel('Number of defaults out of 100 loans')\n",
    "_ = plt.ylabel('Probability')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Will the bank fail?\n",
    "\n",
    "Plot the number of defaults you got from the previous exercise, in your namespace as n_defaults, as a CDF. \n",
    "\n",
    "If interest rates are such that the bank will lose money if 10 or more of its loans are defaulted upon, what is the probability that the bank will lose money?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 189,
   "metadata": {},
   "outputs": [],
   "source": [
    "def ecdf(data):\n",
    "    \"\"\"Compute ECDF for a one-dimensional array of measurements.\"\"\"\n",
    "    # Number of data points: n\n",
    "    n = len(data)\n",
    "    # x-data for the ECDF: x\n",
    "    x = np.sort(data)\n",
    "    # y-data for the ECDF: y\n",
    "    y = np.arange(1, n + 1) / n\n",
    "    return x, y"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 190,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Compute the x and y values for the ECDF of n_defaults\n",
    "x, y = ecdf(n_defaults)\n",
    "#-Plot the ECDF\n",
    "_ = plt.plot(x, y , marker='.', linestyle='none')\n",
    "_ = plt.xlabel('x')\n",
    "_ = plt.ylabel('y')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 191,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of losing money = 0.022\n"
     ]
    }
   ],
   "source": [
    "#Compute the total number of entries in your n_defaults array that \n",
    "#were greater than or equal to 10\n",
    "n_lose_money =np.sum(n_defaults >=10)\n",
    "#fraction of n_defaults\n",
    "print('Probability of losing money =', n_lose_money/len(n_defaults))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability distributions and stories: The Binomial distribution\n",
    "\n",
    "**Probability Mass function(PMF):** is defined as the set of probabilities of discrete outcomes. (each results had the same or uniform probability)\n",
    "\n",
    "**Binomial Distribution:** The number of r of successes in n *Bernoulli trails* with probability p of succes, is Binomially distrubuted."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Sampling out of the Binomial distribution\n",
    "\n",
    "Compute the probability mass function(PMF) for the number of defaults we would expect for 100 loans as in the last section, but instead of simulating all of the Bernoulli trials, perform the sampling using `np.random.binomial()`. This is identical to the calculation you did in the last set of exercises using your custom-written perform_bernoulli_trials() function, but far more computationally efficient. Given this extra efficiency, we will take 10,000 samples instead of 1000. After taking the samples, plot the ECDF as last time. This ECDF that you are plotting is that of the Binomial distribution.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 193,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#set the Seed(42)\n",
    "np.random.seed(42)\n",
    "# Draw samples out of the Binomial distribution\n",
    "n_binomial = np.random.binomial(100, 0.05, size=10000)\n",
    "\n",
    "x, y = ecdf(n_binomial)\n",
    "#Plot the ECDF\n",
    "sns.set()\n",
    "_ = plt.plot(x, y, marker='.', linestyle='none')\n",
    "_ = plt.xlabel('number of succeses')\n",
    "_ = plt.ylabel('CDF')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Plotting the Binomial PMF\n",
    "\n",
    "We will plot the PMF of the Binomial distribution as a histogram. The trick is setting up the edges of the bins to pass to plt.hist() via the bins keyword argument. We want the bins centered on the integers. So, the edges of the bins should be -0.5, 0.5, 1.5, 2.5, ... up to max(n_defaults) + 1.5. You can generate an array like this using np.arange() and then subtracting 0.5 from the array.\n",
    "\n",
    "You have already sampled out of the Binomial distribution during your exercises on loan defaults, and the resulting samples are in the NumPy array n_defaults.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 194,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Using np.arange(), compute the bin edges such that the bins are centered on the integers\n",
    "bins = np.arange(min(n_defaults), max(n_defaults) +1.5) -0.5\n",
    "#plot the histogram of n_defaults\n",
    "_ = plt.hist(n_defaults, bins=bins, density=True)\n",
    "_ = plt.xlabel('x')\n",
    "_ = plt.ylabel('y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Poisson processes and the Poisson distribution\n",
    "\n",
    "**Poisson Process:** The timing of the next event is completely independent of when the previous event happend. \n",
    "\n",
    "The number of r of arrivials of a Poisson process in a given times interval with avarrage rate of $\\lamda$ arrivials per interval is Poisson distrubutions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Relationship between Binomial and Poisson distributions\n",
    "\n",
    "Poisson distribution is a limit of the Binomial distribution for rare events. Let's say we do a Bernoulli trial every minute for an hour, each with a success probability of 0.1. We would do 60 trials, and the number of successes is Binomially distributed, and we would expect to get about 6 successes. This is just like the Poisson story. So, the Poisson distribution with arrival rate equal to np approximates a Binomial distribution for n Bernoulli trials with probability p of success (with n large and p small). Importantly, the Poisson distribution is often simpler to work with because it has only one parameter instead of two for the Binomial distribution.\n",
    "\n",
    "Let's explore these two distributions computationally. You will compute the mean and standard deviation of samples from a Poisson distribution with an arrival rate of 10. Then, you will compute the mean and standard deviation of samples from a Binomial distribution with parameters n and p such that np=10."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 195,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Poisson mean = 9.9732, std = 3.1276319732347027\n"
     ]
    }
   ],
   "source": [
    "#draw 10000 samples from a Poisson distribution with a mean of 10\n",
    "sample_poisson = np.random.poisson(10, size=10000)\n",
    "s_mean =np.mean(sample_poisson)\n",
    "s_std = np.std(sample_poisson)\n",
    "print('Poisson mean = %s, std = %s'%(s_mean, s_std) )"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 196,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "n = 20 , Binom mean = 9.9999 & std =2.243858282066851\n",
      "n = 100 , Binom mean = 9.9957 & std =2.998346462635698\n",
      "n = 1000 , Binom mean = 9.997 & std =3.124162447761\n"
     ]
    }
   ],
   "source": [
    "#Make a list of the n and p values to consider for the Binomial distribution\n",
    "n = [20,100, 1000]\n",
    "p = [0.5, 0.1, 0.01]\n",
    "for i in range(3):\n",
    "    #draw 10000 samples from a Binomial distribution with each n, p pair\n",
    "    samples_binomial = np.random.binomial(n[i], p[i], size=10000)\n",
    "    #print the mean and standard deviation of the samples\n",
    "    b_mean = np.mean(samples_binomial)\n",
    "    b_std =  np.std(samples_binomial)\n",
    "    print('n =',n[i],', Binom mean = %s & std =%s'% (b_mean, b_std) )"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Probability density functions (PDF)\n",
    "\n",
    "**Probability density functions (PDF):** is described the changes of the observing a value of a continues variable. (Continues anaolog to the probability mass functions(PMF)).\n",
    "\n",
    "Let's use the michelson speed of light experiment result to explore the PDF.\n",
    "\n",
    "Areas under the PDF gives the probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 247,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXgAAAEPCAYAAABIut/fAAAABHNCSVQICAgIfAhkiAAAAAlwSFlzAAALEgAACxIB0t1+/AAAADl0RVh0U29mdHdhcmUAbWF0cGxvdGxpYiB2ZXJzaW9uIDIuMi4zLCBodHRwOi8vbWF0cGxvdGxpYi5vcmcvIxREBQAAHy1JREFUeJzt3X1YVGX+P/D3wIAPYauxg7irGZpPtSVel6WYQFgCMjMiRkoSXK0bkqKuaRqwmN8MjTWvLEJbt1V3W+0q08Q0QU1XVEAL10UpSitGS5DnBORpGO7fH/w4iorMwMDozfv1j54z55z7vj8M7zmcOXOPSgghQERE0rGzdQeIiKhzMOCJiCTFgCcikhQDnohIUgx4IiJJMeCJiCTFgCcikhQDnohIUgx4IiJJMeCJiCTFgCcikhQDnohIUgx4IiJJqW3VcHn5VfTrdw9KS6ts1YU7irOzE2txHdajJdbjmu5aCzs7Ffr1u8eifWwW8I2NosW/xFrciPVoifW4hrUwDy/REBFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaRsdh880e38Kf4Aisprurxd53t74q15E7q8XaLOwICnO1JReQ02R0/q8nZnJxzu8jaJOgsv0RARSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKbOmKkhKSkJKSgoAwNvbG8uWLUNMTAxOnTqFXr16AQDmz5+PyZMnd15PiYjIIm0GfEZGBo4fP45du3ZBpVLhxRdfxMGDB5GTk4OtW7fCxcWlK/pJREQWavMSjUajQXR0NBwdHeHg4IChQ4ciPz8f+fn5iI2NhV6vR2JiIhobG7uiv0REZKY2A37YsGFwd3cHABgMBqSkpMDT0xPjx4/H6tWrsX37dmRlZWHHjh2d3lkiIjKf2dMFnz9/HpGRkVi2bBmGDBmC9evXK4+FhYUhOTkZM2bMMLthZ2cnAIBG08eC7sqNtWjJFvVw6dfLZlMGu/TrhU1xvq0+zufHNayFecwK+FOnTmHhwoWIjY2FVqvF999/D4PBAD8/PwCAEAJqtWVTy5eWVsHZ2QnFxZWW91pCGk0f1uIGtqhHQqRHl7fZbHbC4VbHzOfHNd21FnZ2KuXE2Ox92tqgoKAAUVFRWLt2LbRaLYCmQF+9ejWuXLkCo9GITz75hHfQEBHdYdo87d60aRPq6uqQkJCgrAsJCcGcOXPw3HPPoaGhAb6+vtDpdJ3aUSIiskybAR8XF4e4uLhbPhYaGmr1DhERkXXwk6xERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJIyK+CTkpKg1Wqh1WqxZs0aAEBGRgb0ej18fX2xbt26Tu0kERFZrs2Az8jIwPHjx7Fr1y4kJyfjm2++wd69exEbG4sNGzZg3759yMnJQVpaWlf0l4iIzNRmwGs0GkRHR8PR0REODg4YOnQoDAYDBg8ejEGDBkGtVkOv1yM1NbUr+ktERGZqM+CHDRsGd3d3AIDBYEBKSgpUKhU0Go2yjYuLCwoLCzuvl0REZDG1uRueP38ekZGRWLZsGezt7WEwGJTHhBBQqVQWNezs7AQA0Gj6WLSfzFiLlrpjPW435u5Yj9awFuYxK+BPnTqFhQsXIjY2FlqtFl999RWKi4uVx4uLi+Hi4mJRw6WlVXB2dkJxcaVlPZaURtOHtbhBd6xHa2Pm8+Oa7loLOzuVcmJs9j5tbVBQUICoqCisXbsWWq0WADB69Gjk5eXhwoULMJlM2Lt3L7y8vNrXayIi6hRtnsFv2rQJdXV1SEhIUNaFhIQgISEBCxYsQF1dHby9veHv79+pHSUiIsu0GfBxcXGIi4u75WOff/651TtERETWwU+yEhFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpswO+qqoKOp0Ov/zyCwAgJiYGvr6+CAwMRGBgIA4ePNhpnSQiIsupzdkoOzsbcXFxMBgMyrqcnBxs3boVLi4undU3IiLqALPO4Ldv344VK1YoYV5TU4P8/HzExsZCr9cjMTERjY2NndpRIiKyjFln8KtWrWqxXFJSgvHjx2PFihXo06cPIiMjsWPHDsyYMcPshp2dnQAAGk0fC7orN9aipe5Yj9uNuTvWozWshXnMCvgbDRo0COvXr1eWw8LCkJycbFHAl5ZWwdnZCcXFle3pgnQ0mj6sxQ26Yz1aGzOfH9d011rY2amUE2Oz92lPQ99//z3279+vLAshoFa367WCiIg6SbsCXgiB1atX48qVKzAajfjkk08wefJka/eNiIg6oF2n3SNHjsScOXPw3HPPoaGhAb6+vtDpdNbuGxERdYBFAX/48GHl/6GhoQgNDbV6h4iIyDr4SVYiIkkx4ImIJMWAJyKSFAOeiEhSDHgiIkkx4ImIJMWAJyKSFAOeiEhSDHgiIkkx4ImIJMWAJyKSFAOeiEhSDHgiIkkx4ImIJMWAJyKSFAOeiEhSDHgiIkkx4ImIJMWAJyKSFAOeiEhSDHgiIkkx4ImIJMWAJyKSFAOeiEhSDHgiIkmpbd0BunMt3ZCB0opam7Tt0q+XTdrtjmz5c3a+tyfemjfBJm13Bwx4alVpRS02R0+ySdsaTR8UF1fapO3uxpY/59kJh23SbnfBSzRERJJiwBMRScqsgK+qqoJOp8Mvv/wCAMjIyIBer4evry/WrVvXqR0kIqL2aTPgs7Oz8dxzz8FgMAAAamtrERsbiw0bNmDfvn3IyclBWlpaZ/eTiIgs1GbAb9++HStWrICLiwsA4MyZMxg8eDAGDRoEtVoNvV6P1NTUTu8oERFZps27aFatWtViuaioCBqNRll2cXFBYWGh9XtGREQdYvFtko2NjVCpVMqyEKLFsrmcnZ0ANN0OR03uxFrYsk93Yj06k0u/Xja5bdClX6+77ufc3Z4b7WVxwLu6uqK4uFhZLi4uVi7fWKK0tArOzk681/n/u1Pv+7ZVn+7UenSmhEiPVh/r7HrYstaWtt0dnxsAYGenUk6Mzd7H0kZGjx6NvLw8XLhwASaTCXv37oWXl5elhyEiok5m8Rl8jx49kJCQgAULFqCurg7e3t7w9/fvjL4REVEHmB3whw9fuzbo4eGBzz//vFM6RERE1sFPshIRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKQY8EZGkGPBERJJiwBMRSYoBT0QkKYu/k5W63tINGSitqO3ydp3v7dnlbRKR9TDg7wKlFbXYHD3J1t0gorsML9EQEUmKAU9EJCkGPBGRpBjwRESSYsATEUmKd9EQkc0439sTsxMO26Tdt+ZN6PJ2uxoDnohspj0hq9H0QXFxZYfatcWLii3wEg0RkaQY8EREkurQJZqwsDCUlZVBrW46zMqVKzF69GirdIyIiDqm3QEvhIDBYMB//vMfJeCJiOjO0e5LND/99BMAYPbs2Zg6dSq2bt1qtU4REVHHtfvUu6KiAh4eHli+fDmMRiPCw8Ph5uaGJ554wpr9IyKidmp3wI8ZMwZjxoxRloODg5GWlmZ2wDs7OwFouuWJmtyuFt2xTt1xzLfDelxjjVp0h3q2O+CzsrJgNBrh4eEBoOmavCXX4ktLq+Ds7NTh+1ll0da9vd2tTta411kmrMc11qrF3VZPOzuVcmJs9j7tbayyshJr1qxBXV0dqqqqsGvXLkyePLm9hyMiIitr9xm8j48PsrOzMW3aNDQ2NmLWrFktLtkQEZFtdej+xkWLFmHRokXW6gsREVkRP8lKRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQY8EREkmLAExFJigFPRCQpBjwRkaQ69JV9trB0QwZKK2pt0rbzvT3x1rwJNmmbiMhSd13Al1bUYnP0JJu0PTvhsE3aJSJqD16iISKSFAOeiEhSDHgiIkkx4ImIJMWAJyKSFAOeiEhSd91tkkREHeV8b0+b3fbclZ+nYcATUbdjyw8sduULCy/REBFJigFPRCSpDgX8nj17EBAQAF9fX2zbts1afSIiIito9zX4wsJCrFu3Dp999hkcHR0REhKCcePG4cEHH7Rm/4iIqJ3aHfAZGRkYP348+vbtCwDw8/NDamoq5s+fb9b+dnaqFv+ay6VfL4v3sZbObru1Y9tyzLbUHcd8O6zHNXdzLdr7+9yefVRCCGHxXgA2btyI6upqvPzyywCATz/9FGfOnMEbb7zRnsMREZGVtfsafGNjI1Sqa68oQogWy0REZFvtDnhXV1cUFxcry8XFxXBxcbFKp4iIqOPaHfATJkxAZmYmysrKUFNTgwMHDsDLy8uafSMiog5o95us/fv3x8svv4zw8HAYjUYEBwfj0UcftWbfiIioA9r9JisREd3Z+ElWIiJJMeCJiCTFgCcikhQDnohIUu0K+KSkJGi1Wmi1WqxZswYA8NlnnyEgIAB6vR7x8fFoaGgAAJw5cwbPPPMM9Ho9IiMjlXvn6+vrER8fj2nTpkGr1eL48eMAmj4w9de//hX+/v4ICAjAqVOnlHY3b94Mf39/+Pn54cCBAx0auDVZox4vvfQSAgMDERgYCL1ejxEjRuDs2bPdth719fVYsmQJ9Ho9AgMDkZGRoRy/tXHfiZPfWaMWJSUleOmll6DT6TBz5kycPn1aOf7dVAsAePfddxEQEACtVostW7YAaJr2RK/Xw9fXF+vWrVO2zc3NxfTp0+Hn54e//OUvSp3y8/MRGhoKf39/zJ07F1evXgUAVFRUYM6cOZgyZQpCQ0NbPJeWLl2KKVOmICgoCD/++GMXj9qGhIXS09PFzJkzRV1dnaivrxfh4eFi48aNwtPTUxQWFgohhFixYoXYvHmzaGxsFN7e3iIzM1MIIcQXX3whIiMjhRBCrF+/XixevFg0NjaKc+fOiYkTJ4rGxkaRkpIiIiIihMlkEj/99JOYPHmyMBqNIjs7WwQGBora2lpRUlIinnrqKVFeXm5p963OWvW43jvvvCPi4uKEEKLb1mP79u1i0aJFQgghvvvuO+Hp6SmEEK2O+/Lly8LHx0eUl5eLq1evCr1eL86fP2+DClxjrVosWbJEvPvuu0IIIS5evCieeuopUVNTc1fVQgghTp48KUJCQoTRaBQ1NTXCx8dH5ObmCm9vb3Hx4kVhNBrF7NmzxZEjR4QQQmi1WnH69GkhhBAxMTFi27ZtQggh5syZI/bu3SuEECIpKUmsWbNGCCHE66+/LjZu3CiEEGLXrl3iz3/+sxBCiH/84x9i+fLlQgghvvrqK/Hss8923aBtzOIzeI1Gg+joaDg6OsLBwQFDhw5FfX093N3dlU+y+vj44Msvv0R5eTlqa2sxfvx4Zf3x48dRX1+PlJQUREREQKVSYdiwYdiyZQuEEEhLS0NAQADs7Ozg5uaGAQMG4PTp0zh69CgmT56MHj16wNnZGY8//jiOHDli1Re79rBWPZr99NNPSE5OxquvvgoA3bYejY2NqKmpgclkQk1NDXr27AkArY77+snvevfurUx+Z0vWqkVubi6mTJkCABg0aBD69u172+fAnVgLAHj88cfx4YcfQq1Wo7S0FCaTCRUVFRg8eDAGDRoEtVoNvV6P1NRUXLp0CbW1tXB3dwcATJ8+HampqTAajfj666/h5+fXYj0AHDlyBHq9HgCg0+lw9OhRGI1GHDlyBFOnTgUAPPbYYygrK0N+fr4NKtD1LA74YcOGKUU3GAxISUlBQEAAsrOzUVBQAJPJhNTUVJSUlKBfv37o3bu3cvnliy++gNFoRHl5OS5cuICvv/4as2bNwsyZM1FSUgI7OzsUFRW1mPJAo9Hg8uXLra63NWvVo9mGDRvwpz/9CU5OTgDQbesRFBSEX3/9FZ6ennj++efxyiuvALh9PTQajbLexcUFhYWFXTjym1mrFg899BC++OILAMC5c+fwww8/oKSk5K6qRTMHBwckJiZCq9XCw8Oj1b7euF6j0aCwsBDl5eVwcnKCWq1usR5Ai33UajWcnJxQVlZ2y2PdCb8rXaHdb7KeP38es2fPxrJlyzBkyBAsWbIEc+fORWhoKEaMGAEHBweoVCokJiZi48aNmDZtGiorK9G3b184ODjAZDLh8uXL2LZtG15//XW88sorqKysvOUkZnZ2dmhsbLy583Z3znvEHa0HAFy5cgXp6el49tlnleN213okJSXB3d0d6enp2LNnD1atWoVLly61Ou47efK7jtYiJiYGFy5cgF6vx4cffohx48bBwcHhrqwFACxcuBCZmZkoKCiAwWC4ZV9bG8OtxtLa2Jp/V27cp3l9d9CuqQpOnTqFhQsXIjY2FlqtFnV1dXj00UeRnJwMAEhJScGgQYOaGlCr8e9//xsAUFpaig0bNqBv37747W9/C61WC5VKhZEjR8LV1RV5eXlwdXVFUVGR0lZJSQlcXFxuObmZm5tbuwduTdaoB9B0OcbLyws9evRQjt1d63Ho0CGsW7cOKpUKbm5uGD16NM6cOdPquIUQyMrKarH+Tpj8zhq1yM/PxxtvvKH8VafVanH//fffdbX48ccfUV9fj1GjRqFXr17w9fVFamoq7O3tlW2a+3rj2Jqf9/fddx8qKythMplgb2/fYmwuLi4oKSmBq6srGhoacPXqVfTt2xf9+/dHUVER7r///hbH6g4sfhkrKChAVFQU1q5dC61WCwCorq7GCy+8gKqqKtTX12Pr1q0ICAgAAMTGxuLMmTMAgC1btsDf3x92dnbw8fHBvn37AAA///wzCgoK4ObmBi8vL+zZswcmkwkXLlyAwWDAI488Ai8vLxw4cAA1NTUoKyvDiRMn4OHhYa06tJu16gEA//vf/zB27NgWx++u9Rg5ciS+/PJLAEBZWRlycnIwatSoVsd9J05+Z61abN26FR9//DGApvcgTCYTRo4ceVfVAgB++eUXxMXFob6+HvX19Th06BBCQkKQl5eHCxcuwGQyYe/evfDy8sLvf/979OjRQ7lrbPfu3fDy8oKDgwPGjh2rZEdycrIyNm9vb+WFc9++fRg7diwcHBzg7e2N3bt3AwCysrLQo0cP/O53v7NBBbqexXPRxMfHY+fOncqrIQCEhIRArVbjn//8JxoaGqDT6bBgwQIATbd+rVixAjU1NRgxYgRWrVoFJycnVFVVYeXKlfjmm28AAK+88gp8fHwghMCaNWtw9OhRAEBMTAwmTpwIoOmWsJ07d6KhoQFz587FtGnTrFKEjrBWPQAgIiICYWFhLX4Zu2s9SkpKsHz5cly8eBF2dnaIjIyETqcD0Pq49+zZg40bNyqT30VERHR9Aa5jrVqUlZVhyZIlKCkpwT333IP4+HjlqzHvllo0e++995CSkgJ7e3v4+vpiwYIFyMzMxJtvvom6ujp4e3sjJiYGKpUK3333HeLi4lBVVYWHH34Yb775JhwdHXHp0iVER0ejtLQUAwYMwNtvv43f/OY3+PXXXxEdHY2ff/4Zffr0wdq1azFw4EDU1dXhtddeQ05ODhwdHREfH4+HH37Y1qXoEpxsjIhIUt3jnQYiom6IAU9EJCkGPBGRpBjwRESSYsATEUmKAU9teu+997By5cp27Xv27FksXLgQQNNtgK+99prV+rVixQpMmjSpxQyEQMv+RkRE4IcffrjtcaKjo7Fp06ZbPpaUlKTcj3+968dlDYGBgaioqDBr27S0NGXMI0aMQFlZWYfa3rp1621nnPzyyy+xfv36DrVBttHuL90mMscjjzyCxMREAMAPP/xg1TlRPvnkExw5cgSurq6tbvPBBx90qI2TJ08q95xf7/pxWUPzB3HaUlVVhbVr12L79u1Wa/vQoUNYvXp1q48//fTT2LZtG3JzczFq1CirtUudj2fw3cySJUuwefNmZfmjjz7CokWLAACHDx/Gs88+i2nTpiEkJKTFvOPNzp8/j7CwMOj1ekydOlX55CAA7NixA1qtFnq9HuHh4SgoKMDJkyeh0+lQUFCAxMREZGVlISYmBnFxcS3OvHfv3o2oqCiz25s1axaEEIiIiGjxsfwbTZo0CWfPngUA/P3vf4evry+CgoKwatUqTJo0Sdnu9OnTCAkJwdNPP425c+eiuroa27ZtQ05ODtasWYODBw+2OG7zuICmvwDi4+MRFhaGyZMnY/78+coc5dfLy8vDH//4R8yYMQM+Pj6YO3cu6urqAFw7E//ss88wa9YsBAUFISws7KZjfPTRR5g4cSJ69erVYn1xcTF0Op1yJv7II4/g7bffRnBwMAICArBv3z4sXLgQ/v7+CA8PR3V1NYCmOdSrq6sxYMAAZGVlITg4GNOnT8f06dOxf/9+5fjBwcFISkpqtc50h+ra2YnJ1jIzM4VOp1OWg4ODRXp6usjLyxM6nU6UlZUJIYQ4d+6ceOKJJ8TVq1dFYmKieP3114XRaBRPPfWU2L9/vxBCiMuXLwtPT0/x3//+V+Tm5opx48aJ/Px8IYQQW7ZsEcuXLxcnTpwQWq1WCCHEzp07xZw5c4QQQnz77bfiiSeeEEajUQghxKxZs8TRo0db9PV27QkhxPDhw0VpaelNY2zurxBC+Pj4iDNnzoijR48KPz8/ceXKFdHY2ChiYmKEj4+PEEKIV199VQQHB4vq6mrR0NAggoKCxK5du4QQQjz//PMiJSXlpjauH9err77aYt73adOmiR07dty0T0JCgkhOThZCCFFfXy90Op1ITU1tMZadO3eKxx57TFRWVt7y5xcUFCROnDihLA8fPlx8++23IiAgQOzevbvF+n/9619CCCE2btwoxowZIy5fvixMJpMICgoSn3/+uRBCiN27d4ukpCQhhBDh4eHKPOu5ubni//7v/5TjlZeXiz/84Q+ipqbmlv2iOxMv0XQz48aNQ11dHc6ePYtevXqhrKwMHh4e+Oijj1BUVIQXXnhB2ValUuHixYvKssFgQF1dHXx9fQEA/fv3h6+vL44dO4Y+ffpg4sSJGDBgAAAoxzl58uQt+zFq1CgMHDgQR44cgZubG4qKipQpGMxpb8yYMRaNOy0tDf7+/rj33nsBAKGhoThx4oTy+NNPP62cFQ8bNszi69qenp5wdHQEAAwfPhxXrly5aZulS5ciPT0dH3zwAQwGA4qKipQz6euNGDFCmb7iRnl5eRg8eHCLdREREXB1dVXmQm/WPGf6/fffj+HDh6N///4AgIEDByr9O3ToEObNmwcAmDJlClauXInDhw9jwoQJWLx4sXKsvn37okePHrh06RKGDh1qVk3I9hjw3YxKpUJwcDB2794NBwcHBAcHK9Ozenh44J133lG2LSgogIuLi3J5wmQy3TQ1qxACDQ0NsLe3b/FYbW0tLl26dNu+hIaGYufOnXjggQcwY8aMm459u/YspVarIa6bleP6GQybH2/WPC2tJZq/kOR2+y9evBgmkwlTpkzBk08+iYKCgltu17t371bbaf5ZXW/lypX429/+hi1btmD27NnK+uZpqG/8f7P6+noYDAaMGDECQNM8OT4+PkhPT8exY8eQlJSE1NRUZXZTe3v7m+pGdzZeg++GgoKCcPjwYezfvx/Tp08HAHh4eCA9PV35vsq0tDRMnToVtbW1yn5DhgyBWq1WvvuzsLAQ+/fvx4QJEzBu3DhkZmYqUxt//PHHeOutt1q0a29v3yKc/fz8kJubi/379+OZZ565qZ+3a89S3t7eOHDgACorKwE0vV9gjhv73BHHjx9HVFSUMntkdnY2TCaTRcd44IEHWvxVBQDu7u5ISEjA+++/j3Pnzpl9rMzMTOUbpICmgG/+HtQ33ngDFRUVypS9lZWVqK+v7zazMMqCZ/DdkEajwUMPPYSGhgblz/YHH3wQK1euxOLFiyGEgFqtxvvvv4977rlH2c/BwQEbNmxAfHw83nvvPZhMJkRFRSkhsXTpUrz44otKG6tXr4bBYFD2d3d3x/r16zF//nwkJSXB0dERfn5+KCkpwX333XdTP9tqzxIeHh6YMWMGZs6ciZ49e2LYsGE3vVF5K5MmTcLbb78No9GIoKAgi9u93ssvv4yoqCj07t0bTk5OeOyxx24K67b4+/vj2LFjN9VgyJAhmDdvHpYuXYpPP/3UrGMdOnRIeaMYaJrRdfXq1XjnnXegUqkwf/58DBw4EEDTi9OTTz6pXIaiuwNnkySbqa6uxvPPP4/XXntN+Wq7znL27FmcPn0a4eHhAJrmW8/Ozm5xSepuUFVVhRkzZmDnzp1mvUBZS3h4OGJjYzFy5Mgua5M6jpdoyCaOHTuGJ598Ep6enp0e7gDg5uaGrKws6HQ66PV6ZGZmIiYmptPbtTYnJycsXrwY77//fpe1efDgQYwdO5bhfhfiGTwRkaR4Bk9EJCkGPBGRpBjwRESSYsATEUmKAU9EJCkGPBGRpP4f9Pp4XVyPdP0AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Let's use the michelson speed of light data to explore the PDF\n",
    "speed_of_light = pd.read_csv('data/michelson_speed_of_light.csv')\n",
    "#Making a list from velocity of light in air (km/s)\n",
    "speed = list(speed_of_light['velocity of light in air (km/s)'])\n",
    "_ = plt.hist(speed ,histtype='step')\n",
    "_ = plt.xlabel('velocity of light in air (km/s)')\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 243,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x1a22cbc358>"
      ]
     },
     "execution_count": 243,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(speed)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Area under the PDf gives the probablities.So, the probability of measuring the speed of light is greater than 300000km/s is an area under the normal curve is about 3% change, because is about 3% of the total area. To calculate this more clearly we need to makeCumulative Distirbution Function(CDF) for speeds from Michelson experiment."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 244,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#using ecdf function make  ecdf plot\n",
    "x_speed, y_speed = ecdf(speed)\n",
    "\n",
    "_ = plt.plot(x_speed, y_speed)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "CDF gives the probability the measured speed of light will be less than the value on the x-axis. So, reading off the value at 300000 km/s, we see that there is 97% change a speed of light measurment is less than that, So, there is only 3% change it is greater."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Introduction to the Normal distribution\n",
    "**Normal distribution:** Describe a continuous variable whose PDF has a single symmetric paek. it is also called the **GAUSIAN DISTRIBUTION**\n",
    "\n",
    "`The mean` determines where the center of the peak is\n",
    "\n",
    "`The standart deviation` is a measures of how data wide the peak or how spread out the data are.\n",
    "\n",
    "*Let's check the Normality of Michelson data*\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 250,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#mean and standart deviation from Michelson data\n",
    "mean = np.mean(speed)\n",
    "std  = np.std(speed)\n",
    "#sample the michelson data using normal distributin function\n",
    "samples = np.random.normal(mean, std, size=10000)\n",
    "x_theory, y_theory =ecdf(samples)\n",
    "\n",
    "_ = plt.plot(x_speed, y_speed, marker='.', linestyle='none')\n",
    "_ = plt.plot(x_theory, y_theory, color='r')\n",
    "plt.show()\n",
    "#plots shows that speed of light is normaly distributed."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "\n",
    "### The Normal PDF\n",
    "\n",
    "We will explore the Normal PDF and also learn a way to plot a PDF of a known distribution using hacker statistics. Specifically, you will plot a Normal PDF for various values of the variance.\n",
    "\n",
    "*The normal distribution describes a continuous variable whose Probability density function (PDF) has a single symmetric peak*. The Normal distribution is parametrized by two parameters, `The mean`, determines where the centr of the peak. `The standart deviation` is a measure how wide the peak is, or how spread out the data.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 251,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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FhSExMRGNjY0AgNzcXAQEBCAiIgIRERHIyMgwb+2JiMyoO8cjuHTpAt5883U0NjZCrVbjyy8/h4/PCLPsR2cZPCMoLS1FRkYGcnJy4OjoiKioKIwaNQpDhgwBAFy/fh1paWnIzc3FgAEDEB8fj9zcXEydOhWnTp1CYmIiwsPbPn0iIrqdxMWjS3f4dLRdQ555ZipSU5NRUJAPOzu7VuMRJCenYsmSZVixIhWZmRvwyCM+JtfniScC8O23pzFz5jTY2dlh9OixGD8+2OTtdYXBIFAqlfDz84ObmxsAIDg4GIWFhXjxxRcBAM7Ozjh06BAcHBxQX1+P8vJy9O3bFwBw8uRJnD9/Hhs3bsTQoUOxZMkS9OvXz4K7Q0Q9nan3+ptDd49HMGvWHMyaNccs2+oKg0FQVlYGmUymm5bL5Thx4oTeOg4ODvj888+xaNEiyOVyBAQEAABkMhlmzpyJkSNHYvXq1UhLS8Pbbxv/P9nDw8XodS1NJnO1dhVsAtuhWUs7iL09zLH/ZWV2kEp7/n0r1tgHOzs7s/w/MBgEWq0WEolENy0Igt50i9GjR+Orr77C6tWrkZKSgrfffhvr16/XLZ89ezYmTJjQqcqVl9dCqxUMr2hhMpkrVKoaa1fD6tgON7W0g5jbw1zfB61Wi6YmrRlqZD1SqZ1V9kGr1er9P7Czk5j0A9pghHl5eUGlUummVSoV5PKb97pWVVXhyy+/1E0rFAqcPXsWNTU12Lp1q26+IAiwt7fvdAWJiMiyDAaBv78/iouLUVFRgfr6ehQVFSEwMFC3XBAEJCQk4NKlSwCAwsJCjBw5Es7Ozti8eTOOHz8OANi2bVunzwiIiMjyDHYNeXp6Ij4+HjExMVCr1ZgyZQp8fHwQGxuLuLg4DBs2DMuWLcOcOXMgkUgwZMgQpKamwt7eHmvWrEFKSgoaGhpw3333YdWqVd2xT0QWkbBBadQA6EQ9jVEPlCkUCigUCr15mZmZur/Hjx+P8ePHtyrn6+uL3FzrPClHZG7l1xrwfuJYa1eDyOz4ZDER2ZQlyhWoaKg0+3bdnfpjmf/fTCprqddQA0BdXS3mzp2JVavWYODAuwAAR49+hXXrMnDjxg2MHTsBzz8/3+TtG4NBQEQ2paKhEuvHmr8b+YVDi0wua4nXUAPA6dOnsGrVcvz66y+6eTduNGDFijSsW7cJcrknFi16GcXF/8QTTzxp9s9vwSAgIvpNd76GGgDy83Pxyit/xbJlr+nmffvtadxzz724665BAICgoBB89tmnDAIiou7Q3a+hTkxc0mre1asqeHgM0E17eAyASlVm+k4ZgUFAZCKOUtb7+Po+jqSkRfj++7Pw9w8w6jXU+/btabUdY88I2tL80K7eHEgkln1qmUFAZCKOUtb7dOdrqNsjk8lx9erNMZvLy8sxYMCADkp0Xc9/wQcRkZl052uo2/Pww9749defceHCr9BoNPjkkwPw87Pc9QGAZwRERDrd+Rrq9txxxx1YvHgpkpIWobHxBp544kmMGTPO7J9zKwYBEdkUd6f+XbrVs6PtGtLdr6FusWtXvt60r+/j+Pvft5v1MzrCICAim2LqQ19kOl4jICISOQYBEZHIMQiIyOpuvSWTjCMIWgCtBwkzBYOAiKxKKnVEXd01hoGRBEFAU5MaVVVX4ehontei82IxEVlV//4yVFaqUFtbZe2qmMzOzg5abfcNVWlnZ48+fVzg4tLPLNtjEBCRVdnbSzFgwEBrV6NLevp43kZ1DeXn5yM0NBRBQUHIyspqtfyTTz6BQqFAWFgYEhMT0djYCAC4dOkSpk2bhokTJ2LevHmoq6szb+2JiKjLDAZBaWkpMjIykJ2djby8POzYsQPnzp3TLb9+/TrS0tLwwQcfYP/+/bhx44ZuVLLU1FRER0ejsLAQ3t7e2LBhQ3sfQ0REVmIwCJRKJfz8/ODm5gZnZ2cEBwejsPDm+zWcnZ1x6NAhDBgwAPX19SgvL0ffvn2hVqtx9OhRBAcHAwAiIyP1yhERkW0wGARlZWWQyWS6ablcjtLSUr11HBwc8Pnnn+O///u/UVlZiYCAAFRWVsLFxQVSafNlCJlM1qocERFZn8GLxVqtFpJbXo7d/K7s1veujh49Gl999RVWr16NlJQULFq0qNV6bZXriIeHS6fWtySZzNXaVbAJYm+Hlv2/tR3E3CZi3vfb9eS2MBgEXl5eKCm5OQKPSqWCXC7XTVdVVeHUqVMICAgAACgUCsTHx8Pd3R01NTXQaDSwt7dvVc4Y5eW10Gqtf29xT78jwFzYDoBKVdOqHcTaJvw+3GQrbWFnJzHpB7TBriF/f38UFxejoqIC9fX1KCoqQmBgoG65IAhISEjApUuXAACFhYUYOXIkHBwc4Ovri4KCAgBAXl6eXjkiIrINBoPA09MT8fHxiImJweTJkxEeHg4fHx/Exsbi5MmT6N+/P5YtW4Y5c+Zg0qRJ+Omnn5CQkAAAWLp0KXbu3InQ0FCUlJTg5ZdftvgOERFR5xj1QJlCoYBCodCbl5mZqft7/PjxGD9+fKtygwYNwocfftjFKhIRkSXxXUNERCLHICAiEjkGARGRyDEIiIhEjkFARCRyDAIiIpFjEBARiRyDgIhI5BgEREQixyAgIhI5BgERkcgxCIiIRI5BQEQkcgwCIiMkbFDCo6+TtatBZBEMAiIjlF9rwFvz/a1dDSKLYBAQEYmcUUGQn5+P0NBQBAUFISsrq9XyTz/9FBEREZg0aRLmz5+P6upqAEBubi4CAgIQERGBiIgIZGRkmLf2RETUZQZHKCstLUVGRgZycnLg6OiIqKgojBo1CkOGDAEA1NbWIiUlBbt374anpyfeeecdrF27FsnJyTh16hQSExMRHh5u8R0hIiLTGDwjUCqV8PPzg5ubG5ydnREcHIzCwkLdcrVajaVLl8LT0xMAMHToUFy+fBkAcPLkSeTm5kKhUGDhwoW6MwUiIrIdBoOgrKwMMplMNy2Xy1FaWqqb7t+/PyZMmAAAaGhowKZNm3TjF8tkMsyfPx979+7FwIEDkZaWZu76ExFRFxnsGtJqtZBIJLppQRD0plvU1NTghRdewIMPPoinn34aALB+/Xrd8tmzZ+sCw1geHi6dWt+SZDJXa1fBJoi5HW7d9/b+Fhsx7/vtenJbGAwCLy8vlJSU6KZVKhXkcrneOmVlZZg1axb8/PywePFiAM3BsHv3bsyYMQNAc4DY29t3qnLl5bXQaoVOlbEEmcwVKlWNtathdWJvh5Z9v70dxNomYv8+3MpW2sLOTmLSD2iDXUP+/v4oLi5GRUUF6uvrUVRUhMDAQN1yjUaDuXPnIiQkBElJSbqzBWdnZ2zevBnHjx8HAGzbtq3TZwRERGR5Bs8IPD09ER8fj5iYGKjVakyZMgU+Pj6IjY1FXFwcrly5gm+//RYajQYHDhwAAHh7e+P111/HmjVrkJKSgoaGBtx3331YtWqVxXeIiIg6RyIIgvX7XtrBriHbIuZ2mLnyEN5PHAtAvx0SNigBQJRPHYv5+3A7W2kLi3UNEVH73prvj/JrDdauBlGXMAiIiESOQUBEJHIMAiIikWMQEBGJHIOAiEjkGARERCLHICAiEjkGARGRyDEIiIhEjkFARCRyDAIiIpFjEBARiRyDgIhI5BgEREQixyAgIhI5o4IgPz8foaGhCAoKQlZWVqvln376KSIiIjBp0iTMnz8f1dXVAIBLly5h2rRpmDhxIubNm4e6ujrz1p6IiLrMYBCUlpYiIyMD2dnZyMvLw44dO3Du3Dnd8traWqSkpGDTpk3Yu3cvhg4dirVr1wIAUlNTER0djcLCQnh7e2PDhg2W2xMiIjKJwSBQKpXw8/ODm5sbnJ2dERwcjMLCQt1ytVqNpUuXwtPTEwAwdOhQXL58GWq1GkePHkVwcDAAIDIyUq8cUU+RsEEJj75O1q4GkcUYDIKysjLIZDLdtFwuR2lpqW66f//+mDBhAgCgoaEBmzZtwvjx41FZWQkXFxdIpVIAgEwm0ytH1FOUX2sQ5ZjEJB5SQytotVpIJBLdtCAIetMtampq8MILL+DBBx/E008/jdLS0lbrtVWuI6YMwmwpMpmrtatgE8TaDrfvt6FpsRDrfrelJ7eFwSDw8vJCSUmJblqlUkEul+utU1ZWhlmzZsHPzw+LFy8GALi7u6OmpgYajQb29vZtljOkvLwWWq3QqTKWIJO5QqWqsXY1rE7M7XDrfrfVDmJsFzF/H25nK21hZycx6Qe0wa4hf39/FBcXo6KiAvX19SgqKkJgYKBuuUajwdy5cxESEoKkpCTdr34HBwf4+vqioKAAAJCXl6dXjqi38OjrhIQNSmtXg8hkBs8IPD09ER8fj5iYGKjVakyZMgU+Pj6IjY1FXFwcrly5gm+//RYajQYHDhwAAHh7e+P111/H0qVLkZiYiHfffRcDBw7E6tWrLb5DRN3trfn+mLnykLWrQWQyg0EAAAqFAgqFQm9eZmYmAGDYsGE4c+ZMm+UGDRqEDz/8sItVJCIiS+KTxUREIscgICISOQYBEZHIMQiIiESOQUBEJHIMAiIikWMQEBGJHIOAiEjkGARERCLHICAiEjkGARGRyDEIiIhEjkFARCRyDAIiIpFjEBARiRyDgIhI5BgEREQiZ1QQ5OfnIzQ0FEFBQcjKymp3vUWLFiEnJ0c3nZubi4CAAERERCAiIgIZGRldrzEREZmVwaEqS0tLkZGRgZycHDg6OiIqKgqjRo3CkCFD9NZZunQpiouL4efnp5t/6tQpJCYmIjw83DK1JyKiLjN4RqBUKuHn5wc3Nzc4OzsjODgYhYWFeuvk5+dj3LhxCAkJ0Zt/8uRJ5ObmQqFQYOHChaiurjZv7YmIqMsMnhGUlZVBJpPppuVyOU6cOKG3zuzZswEAx44d05svk8kwc+ZMjBw5EqtXr0ZaWhrefvttoyvn4eFi9LqWJpO5WrsKNkGs7XD7frfVDmJsGzHuc3t6clsYDAKtVguJRKKbFgRBb7oj69ev1/09e/ZsTJgwoVOVKy+vhVYrdKqMJchkrlCpaqxdDasTczvcut/ttYPY2kbM34fb2Upb2NlJTPoBbbBryMvLCyqVSjetUqkgl8sNbrimpgZbt27VTQuCAHt7+05XkIiILMtgEPj7+6O4uBgVFRWor69HUVERAgMDDW7Y2dkZmzdvxvHjxwEA27Zt6/QZARERWZ7BriFPT0/Ex8cjJiYGarUaU6ZMgY+PD2JjYxEXF4dhw4a1Wc7e3h5r1qxBSkoKGhoacN9992HVqlVm3wEiIuoag0EAAAqFAgqFQm9eZmZmq/VWrlypN+3r64vc3NwuVI+IiCyNTxYTEYkcg4CISOQYBESd9Mu6uajNftXa1SAyGwYBUSe0BIBQW27lmhCZD4OAyAi12a+iZtMMAMC9L74HiYsHzwqo1zDqriEisRNqy+H6/FbdtEv027pgIOrpGAREXXDzrCDMqvUg6gp2DRGZSOLiofv7tX67rVgToq7hGQGRiVyib75JV2A3EfVgPCMgMuC1frv1fv0T9TYMAiIDPOzr9H79t6VccyfvIqIei0FAZAZp1c/w2QLqsXiNgKgDv258EYALeu7YU0SGMQiIOuAmqdV7fqA9Hn2dLF8ZIgth1xBRO2qzX0W55k6j1n1rvr+Fa0NkOQwConYIteVIq37G6PV5wZh6KqOCID8/H6GhoQgKCkJWVla76y1atAg5OTm66UuXLmHatGmYOHEi5s2bh7q6uq7XmMhG8YIx9VQGg6C0tBQZGRnIzs5GXl4eduzYgXPnzrVaZ+7cuThw4IDe/NTUVERHR6OwsBDe3t7YsGGDeWtPZCG12a+a9OwAX0ZHPZHBIFAqlfDz84ObmxucnZ0RHByMwsJCvXXy8/Mxbtw4hISE6Oap1WocPXoUwcHBAIDIyMhW5YhslVBbbvDZgba4RL/NswLqcQzeNVRWVgaZTKablsvlOHHihN46s2fPBgAcO3ZMN6+yshIuLi6QSps/QiaTobS01CyVJrIkU88GiHoqg0Gg1WohkUh004Ig6E23p631jCl3Kw8Pl06tb0kyGe8kB8TRDjW15bg/6eZL5Nra5/baQSZzRU0Hy3sbseynMXpyWxiCwWkZAAAOlUlEQVQMAi8vL5SUlOimVSoV5HK5wQ27u7ujpqYGGo0G9vb2Rpe7VXl5LbRaoVNlLEEmc4VKVWPtalidmNrh1v28fZ87ageVqgYSFw/89M7zJnUt9SRi+j4YYittYWcnMekHtMFrBP7+/iguLkZFRQXq6+tRVFSEwMBAgxt2cHCAr68vCgoKAAB5eXlGlSPq6XidgHoag0Hg6emJ+Ph4xMTEYPLkyQgPD4ePjw9iY2Nx8uTJDssuXboUO3fuRGhoKEpKSvDyyy+breJERGQeRr1iQqFQQKFQ6M3LzMxstd7KlSv1pgcNGoQPP/ywC9UjIiJL45PFREQixyAgIhI5BgHRLcz1DAGfMKaehEFAdItbnyhO2KA0+fXSvHOIehIGAVE7yq818PXSJAoMAqLf8NUSJFYMAqLfmPqiufbwOgH1FAwCIljmbIDXCainYBAQwTxnAx59nZCwQWmmGhF1HwYBkZm8Nd8f5dca9Oaxe4h6AgYBkQWxe4h6AgYBEZHIMQiIiESOQUBEJHIMAhI9PkhGYmfUeAREvZlQWw7X57dauxpEVmPUGUF+fj5CQ0MRFBSErKysVsu/++47REZGIjg4GElJSWhqagIA5ObmIiAgABEREYiIiEBGRoZ5a0/UA/AWUrJ1BoOgtLQUGRkZyM7ORl5eHnbs2IFz587prZOQkIDXXnsNBw4cgCAI2LlzJwDg1KlTSExMxJ49e7Bnzx7Ex8dbZi+ITNQd3UK8hZRsncEgUCqV8PPzg5ubG5ydnREcHIzCwkLd8osXL6KhoQEjRowAAERGRuqWnzx5Erm5uVAoFFi4cCGqq6sttBtEpjH3+4WIeiKDQVBWVgaZTKablsvlKC0tbXe5TCbTLZfJZJg/fz727t2LgQMHIi0tzZx1J+qS7rxIzO4hsmUGLxZrtVpIJBLdtCAIetMdLV+/fr1u/uzZszFhwoROVc7Dw6VT61uSTOZq7SrYhN7UDjW15bg/aXeH67S3vx21Q1vLZAs24cfXn+lV7Qf0ru9DV/XktjAYBF5eXigpKdFNq1QqyOVyveUqlUo3ffXqVcjlctTU1GD37t2YMWMGgOaAsLe371TlystrodUKnSpjCTKZK1SqGmtXw+p6YzsY2p+2lhtqh/aWSVw88NM7z/earqje+H0wla20hZ2dxKQf0Aa7hvz9/VFcXIyKigrU19ejqKgIgYGBuuWDBg3CHXfcgWPHjgEA9uzZg8DAQDg7O2Pz5s04fvw4AGDbtm2dPiMg6k1aAoBdRGRrDAaBp6cn4uPjERMTg8mTJyM8PBw+Pj6IjY3FyZMnAQDp6elYsWIFJk6ciOvXryMmJgb29vZYs2YNUlJSEBISgtOnTyMhIcHiO0RkDGs9RMY7iMgWGfVAmUKhgEKh0JuXmZmp+/vBBx/Erl27WpXz9fVFbm5uF6tIZH6GHiLrysD1RD0NnywmakP5tQa8nzgWS5QrUNFQaXS5Po8DLxxqvn3a3ak/lvn/zVJVJDIbBgER0OqA33JAd3fqj/VjV+mt29GFwZYRyt6a748lyhV44dAiAAwFsm0SQRCsf1tOO3jXkG3pTe1Qs2kGVnkP1R38bz9Qz1x5CO8njm2zrKF2aKtse2cWPTkgetP3oatspS1MvWuIZwTUq7XbtTNEDneg1a99S7n1YF+zaYbu+gTPGsgWMAio17n14N9W186tB2JraHnK2CX6bb0Df0sgEHU3BgH1CoYO/i1sYewBl+i3UbNpRqv57k79eXZAVsEgoF6hoqHSYDdPy4NctvBk761nBS1uPfCzy4i6E4OAeqzbzwIMsaUBaFyi30Zt9qutwqAFQ4G6E4OAbF5Hd9xY4mJvdz1M1l4X0e0YCmRpDAKyecZ0+5hTy8NktoihQJbAICCb1Nlun56qrWsFxmIokLkwCMhmGHvnT2fVZr8Koba82+4W8ujrhIQNSrw139/guoauFRiLoUBdwSAgq7LUwb9Fy51C3XmR+K35/pi58pDR6xt7rcBYDAXqLAYBdTtLH/xb2NLtooZ0pYuoIwwFMgaDgLpFdx38b2VLt4saYq4uoo4wFKg9DAIyq+6+1dPcrDkOgbm7iDrSXigADAYxYhBQl1nj135HunJx2Fy3jnbmgvGtLNVF1JHbD/o8WxAfo4IgPz8f7777LpqamjB9+nRMmzZNb/l3332HpKQk1NXVwdfXF6mpqZBKpbh06RISEhJQXl6O//qv/0J6ejruvPNOi+wIWd4L+UlQXa9oNd8WDv4trHFxuC2dvWDcoju6iAzp6GyhhbtTf7wX8UZ3VossyOB4BKWlpXj22WeRk5MDR0dHREVFYfXq1RgyZIhunfDwcCxfvhwjRozA4sWL4e3tjejoaMyZMweTJk1CWFgY1q9fj+vXr3dq3GKOR2Ad7XXvyJzdkeKXaIUaGXbrWYCpB9BbB5XpiLHfB2O31xZz7I8l9cbxFbrCVo4Rpo5HYDAIcnNzcfToUbzxRnP6r1+/HoIg4MUXXwQAXLx4EdOnT8enn34KACgpKcH//M//YMuWLRg1ahS+/vprSKVSXL58GX/+859x8OBBoyvHIDCPzg632N4/Zltrh5aDJYAuHzA7c9DuTDt0JQwA8+6jubXVDp39rt2qJ4eIrfzbsNjANGVlZZDJZLppuVyOEydOtLtcJpOhtLQUlZWVcHFxgVQq1ZvfGabsUIudp/Zh1+n9JpfvTWTO7tg59V3zbEvmapbtGFJxZAeqvtjZ4TrSfjLcm7Tb5M/IPnAG24vOAgDk/ftgS3KQ0WWNbYetS4Mxa3mRrpvo2aChiA5+0PjPWbBJ9/cv6+YavJjs9tSf4B441ejtd9Xt7dCV7qIX8pM4JsNvpjwShj95h3fb5xkMAq1WC4lEopsWBEFvur3lt68HoNW0IV05IxjjORpjPEebVPZ2tpL2XWGO+ndrOzwUCteHQg2u1pX6TBg5CBNGDur0tjrbDivnPKE3bWqd+0x9y+A6mi5sv7PM/X2w1W5HY1ji34Yp2zP1jMDO0ApeXl5QqVS6aZVKBblc3u7yq1evQi6Xw93dHTU1NdBoNG2WIyIi22AwCPz9/VFcXIyKigrU19ejqKgIgYGBuuWDBg3CHXfcgWPHjgEA9uzZg8DAQDg4OMDX1xcFBQUAgLy8PL1yRERkGwxeLAaabx/duHEj1Go1pkyZgtjYWMTGxiIuLg7Dhg3DmTNnkJycjNraWjzyyCNYsWIFHB0dcfHiRSQmJqK8vBwDBw7E6tWr0a9fP6MrV1lZZxMXiz08XFBeXmvtalgd26EZ26EZ2+EmW2kLOzsJ+vfv/C36RgUBERH1Xga7hoiIqHdjEBARiRyDgIhI5BgEREQixyAgIhI5BgERkcgxCIiIRI5BQEQkcgwCIiKRYxB04NixY5gyZQoiIiIwffp0XLx4EQBw7do1PP/88wgJCcG0adP0XrrXW+Xn5yM0NBRBQUHIysqydnW61bp16xAWFoawsDCsWtU8EptSqYRCoUBQUBAyMjKsXMPu8+abbyIxsfktod999x0iIyMRHByMpKQkNDU1Wbl23ePQoUOIjIxESEgIli9fDqAXfB8EateYMWOE7777ThAEQfjoo4+EuXPnCoIgCKmpqcLGjRsFQRCE3NxcYcGCBVarY3e4cuWKMGbMGKGyslKoq6sTFAqF8MMPP1i7Wt3in//8pzB16lThxo0bQmNjoxATEyPk5+cLo0ePFn755RdBrVYLM2fOFA4fPmztqlqcUqkURo0aJfz1r38VBEEQwsLChH//+9+CIAjC3/72NyErK8ua1esWv/zyixAQECBcvnxZaGxsFJ599lnh8OHDPf77wDOCdjQ2NmLBggV48MHmQUSGDh2Ky5cvAwAOHz4MhUIBoHmYziNHjkCtVlutrpamVCrh5+cHNzc3ODs7Izg4GIWFhdauVreQyWRITEyEo6MjHBwc8MADD+D8+fMYPHgw7rnnHkilUigUil7fHlVVVcjIyMDcuXMBNI9M2NDQgBEjRgAAIiMje30bAMAnn3yC0NBQeHl5wcHBARkZGejTp0+P/z4wCNrh6OiIiIgIAM2D76xbtw7jx48HoD8qm1QqhYuLCyoqWg/q3lu0NUpdZ0eb66l+97vf6Q5258+fx8cffwyJRCK69njttdcQHx+Pvn37Amh/ZMLe7ueff4ZGo8HcuXMRERGB7OzsXvHvw+AIZWLw8ccfY8WKFXrz7r//fmzduhWNjY1ITExEU1MT5syZ02Z5QRBgZ9d7M9XQKHVi8MMPP2DOnDlYtGgR7O3tcf78ed2y3t4eH330EQYOHIgnnngCOTk5AMT7ndBoNCgpKcGHH34IZ2dnzJs3D05OTj2+LRgEAEJCQhASEtJqfl1dHebNmwc3Nze8++67cHBwANCc+FevXoWXlxeamppQV1cHNze37q52t/Hy8kJJSYluWmyjzR07dgxxcXFYvHgxwsLC8PXXX3c4al9vU1BQAJVKhYiICFRXV+P69euQSCRtjkzY2w0YMABPPPEE3N3dAQDjx49HYWEh7O3tdev0xO9D7/0ZawYJCQkYPHgw1qxZA0dHR9380aNHIy8vD0DzPxJfX19dSPRGhkap680uX76MF154Aenp6QgLCwMADB8+HD/99JOum2Dfvn29uj0++OAD7Nu3D3v27EFcXBzGjh2LFStWtDkyYW83ZswYfPnll7h27Ro0Gg2++OILTJw4scd/H3hG0I5vv/0WBw8exJAhQ/D0008DaD4TyMzMxIIFC5CYmIiwsDC4uroiPT3dyrW1LE9PT8THxyMmJkY3Sp2Pj4+1q9UttmzZghs3bmDlypW6eVFRUVi5ciVeeukl3LhxA6NHj8bEiROtWEvrSE9P1xuZMCYmxtpVsrjhw4dj9uzZiI6OhlqtxpNPPolnn30W999/f4/+PnCEMiIikWPXEBGRyDEIiIhEjkFARCRyDAIiIpFjEBARiRyDgIhI5BgEREQixyAgIhK5/wfnL4xF6A/bDgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Draw 100,000 samples from a Normal distribution \n",
    "#First samplehas a mean of 20 and a standard deviation of 1\n",
    "sample_std1  =  np.random.normal(20, 1,   size=100000)\n",
    "#Second has standard deviations of 3 \n",
    "sample_std3  =  np.random.normal(20, 3,   size=100000)\n",
    "#Third has standard deviations of 10\n",
    "sample_std10 =  np.random.normal(20, 10,  size=100000)\n",
    "\n",
    "#Plot a histograms of each of the samples; for each, use 100 bins\n",
    "_ = plt.hist(sample_std1,  density=True, histtype='step', bins=100)\n",
    "_ = plt.hist(sample_std3,  density=True, histtype='step', bins=100)\n",
    "_ = plt.hist(sample_std10, density=True, histtype='step', bins=100)\n",
    "\n",
    "_ = plt.legend(('std = 1', 'std = 3', 'std = 10'))\n",
    "_ = plt.title(\"The normal distribution\")\n",
    "plt.ylim(-0.01, 0.42)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### The Normal CDF\n",
    "\n",
    "Now that you have a feel for how the Normal PDF looks, let's consider its \n",
    "Cumulative Distirbution Function (CDF). Using the samples `samples_std1`, `samples_std3`, and `samples_std10`.Let's generate and plot the CDFs."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 252,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/evRojB49WtrCjNFoarqMrl27M/R9IIoiHA47rly5iOjo8J0lRd7x1scULoq90jY+3oSLF61obLwUstfU6/UQhMg9aKvXG9ClSzd069Yj3KWo1kvdpb3CtjV29yQ3xQa+wWBEz563hvQ1lXQUnpRJH+TdLNjdUzjxZixECsDunkKBgU/UDk8XXXni6xk67O4p3Bj4RGHG7p5ChYFPFALs7kkJGPhEPnqp+9sBHbTlRVakFAx8Ih8Fe4bOzWYOeEjaHRJ5wcAnklFH3f3I24aHsBIiBj5RUAL9litO5VA4MPCJiDSCgU8kk/amc9jdU7gw8ImINIKBT+SDl7q/DX9u2tped58ce7tEFRH5j4FP5AOpTslcfO/T0uyIKAAMfCKJ8apaUioGPlGA/D0lkwdrKdwY+EQSYndPSsbAJwoBdvekBAx8IomwuyelY+ATeeHvKZk3Y3dPSsHAJ/LiximZHYU+u3uKBAx8IhmxuyclYeATBSDQu2QShRMDn8iDOcW7fH4ub5JGkYKBT0SkEQx8oiDwYC1FEgY+UQee6745oFMyOZ1DSsTAJ+pAD/11AJ5PyWR3T5GGgU8kMXb3pFQ+BX55eTkmTJiA8ePHY+PGjW3Wnzx5Eo888gjuv/9+zJ07Fw0NDZIXSqQUsfM2sLuniOQ18C0WC0pKSrBp0yZs3boVmzdvxokTJ1zrRVHEggULkJubi+3bt+MnP/kJSktLZS2aSKnY3ZOSeQ38qqoqpKWlIS4uDjExMcjIyEBFRYVr/cGDBxETE4NRo0YBAObPn49Zs2bJVzEREQXEa+DX1tbCZDK5ls1mMywWi2v5zJkz6NmzJ5YsWYIHH3wQK1asQExMjDzVEikAL7SiSGX09gRBEKBrdYqCKIpuy3a7HZ999hneeecdpKSk4OWXX0ZxcTGKi4t9LiIhoZufZcvHZIoNdwmKwHHwn5rHTM3vzR+RPg5eAz8pKQn79u1zLVutVpjNZteyyWRCcnIyUlJSAACTJk1CXl6eX0VcuNAIQRD92kYOJlMsrNYr4S4j7DgOTp5ui1zwo1vafb5ax4yfBycljYNerwuoUfY6pZOeno69e/eivr4ezc3NqKysdM3XA8DQoUNRX1+PI0eOAAB27dqFQYMG+V0IkdJ4vC2y3vOPDKdzKBJ47fATExORn5+PnJwc2Gw2TJ06FampqcjNzUVeXh5SUlLw+9//HkuXLkVzczOSkpLw4ov88JO6iGLH98MnigQ6URTDPpfCKR1l4Tg475ZZEuec0tHpnIH/7J23AMa2PZLau3t+HpyUNA6yTekQ0ffamc4hihT8BBP54Nk7b+GcDkU8Bj6RL3iwllSAgU/kRcGP2N2TOjDwiTxwOwff4/mZ7O4p8jDwiTxoJ+OJIhoDn6gD7U3nsLunSMTAJ+oIW31SEQY+0U3mFO8CwFMxSX0Y+ETt4cFaUhkGPpEHS/rc1N2H/w4kREFj4BPd5KXub7O7J1Vi4BPdpM1FtezuSSUY+EQ3aTOdAwCiyO6eIh4Dn+hmnqZzeKdMUgF+iolaeXLXYh6sJdVi4BN5clPoczqH1ICBT/S9J3ctdn/gRncvCKEvhkgGDHyim93U3a85WR++WogkxMAn8oTdPakQA58IraZzWh+kFUUUfcPuntSDgU/UGm+WRirGwCfN83awlrM6pBYMfCJPvp/OEUXg15dzwl0NkSQY+ESt8WAtqRgDnzStzXQOAIgiik/xYC2pDwOf6Gbs7kmlGPikWe119zwVk9SKgU90A2+URirHwCdN8tjdA4Ag8FR8Ui0GPtENrQ7W8mQdUiOfAr+8vBwTJkzA+PHjsXHjxnaft3v3bowdO1ay4ojk0FF33xrPwSe1MXp7gsViQUlJCT744ANER0djxowZGD58OPr16+f2vLq6OrzwwguyFUokt+JTzgutOKVDauW1w6+qqkJaWhri4uIQExODjIwMVFRUtHne0qVL8dRTT8lSJBERBc9rh19bWwuTyeRaNpvNOHDggNtz3n77bdx1110YPHhwQEUkJHQLaDs5mEyx4S5BEdQ6DtM2L/D4+Jbp63Fy9UPtbqfW8fCV1t//DZE+Dl4DXxAE6Fr9jSuKotvysWPHUFlZiQ0bNuD8+fMBFXHhQiMEIfynxJlMsbBar4S7jLDT4jh0FPZvFozV3Hi0psXPgydKGge9XhdQo+x1SicpKQlWq9W1bLVaYTabXcsVFRWwWq146KGHMG/ePNTW1iI7O9vvQojk1u7B2lY4f09q5jXw09PTsXfvXtTX16O5uRmVlZUYNWqUa31eXh527tyJbdu2obS0FGazGZs2bZK1aCIp3fwF5Twlk9TKa+AnJiYiPz8fOTk5eOCBBzBp0iSkpqYiNzcXX331VShqJAqaL919azwlk9TI6xw+AGRlZSErK8vtsbKysjbP6927N3bt2iVNZUQhcHN3T6RmvNKWiEgjGPikeu1N57C7J61h4BMRaQQDn1Stve7eAIPr/6+UPhqiaojCi4FPmrRubFG4SyAKOQY+qZa/p2ICPAef1I2BT5rj7WAtz8EntWLgkyoF0t0TqR0DnzSFp2KSljHwSXXY3RN5xsAnzfDU3fOUTNISBj6pCrt7ovYx8EkT/Jm75ymZpFYMfFINKbp7npJJasbAJ9XztbsXw/8tm0SyYuATEWkEA59UgbdAJvKOgU+a5cspmW8WjJW/EKIQYeBTxOOpmES+YeCTagUyncNTMknNGPgU0aTs7nlKJqkdA59UiQdridpi4FPE4tw9kX8Y+BSROgp7X7p73jSNtIiBT6qSFGMOdwlEisXAp4jTUXe/LO0/A94vz9AhtWPgk2oEe6CWZ+iQ2jHwKaLwQC1R4Bj4pAo8DZPIOwY+RQx290TB8Snwy8vLMWHCBIwfPx4bN25ss/6vf/0rJk+ejPvvvx9PPPEEGhoaJC+UqD3+dvc8JZO0ymvgWywWlJSUYNOmTdi6dSs2b96MEydOuNY3NjbiueeeQ2lpKbZv344BAwbglVdekbVo0h5290TB8xr4VVVVSEtLQ1xcHGJiYpCRkYGKigrXepvNhhUrViAxMREAMGDAAJw7d06+iola4dw9ke+8Bn5tbS1MJpNr2Ww2w2KxuJbj4+Px85//HABw7do1lJaWYty4cTKUSloViu5+YT1PyST1M3p7giAI0Ol0rmVRFN2Wb7hy5QqefPJJDBw4EA8++KBfRSQkdPPr+XIymWLDXYIiKGUcpm1e0O66LdPXB7TPK348VynjEG4cB6dIHwevgZ+UlIR9+/a5lq1WK8xm98vXa2trMXfuXKSlpWHJkiV+F3HhQiMEIfzfIG0yxcJq9ScO1CkSxiE59vaAavT3gK3SxyEUIuHzEApKGge9XhdQo+x1Sic9PR179+5FfX09mpubUVlZiVGjRrnWOxwOzJ8/H5mZmSgsLPTY/RMFoqOpnMX3Pi3765e/NFn21yAKJa8dfmJiIvLz85GTkwObzYapU6ciNTUVubm5yMvLw/nz53Ho0CE4HA7s3LkTAHD33Xdj9erVshdP6hXs3TCJqC2vgQ8AWVlZyMrKcnusrKwMAJCSkoIjR45IXxlRiMTO2wAU7wp3GUSy45W2pDjs7onkwcAnRZEz7HmFLWkdA5+ISCMY+KQYnMohkhcDnxQhXGEfO2+DbPsmUhoGPoUdb4xGFBoMfFI0qbp7HrAlYuBTmHHenih0GPgUNgx7otBi4FNYKGHe/sYB2zm8ypY0goFPIect7KXu7jl/T+TEwKeQCnXYE9EPGPikGEoK+zcLxoa7BCLJMfApZJR0kJYXXJEWMfApJMIV9py/J/oBA59k11HYG2AIYSVE2sbAJ1l5O0i7bmxRiCohIp++8YrIX76cZy/3vH170zmcvyetYodPklNC2BNRWwx8klSkhT2vsiUtYeCTZJQU9pzOIWqLc/gUNF/vi6Okzp5Iixj4FBQldfU3BHvuPa+yJbVi4FNAIrGr53QOaR0Dn/ziz22NwxH2vLKWqH0MfPKJv/evV1JnD3ju7ldt+Dz0hRCFEQOfOhRJQe9vd//N+SvyFEKkUAx8amPa5gV+b5McezsW3/u0DNUEj3P3RE4MfAIQ3FcOKmH6Rqq5e56hQ2rGwNcoKb5TVglBD3Qc9u1197zClrSIga8BUn9heCQEPRG15VPgl5eXY/369bDb7Zg9ezZmzZrltv7w4cMoLCxEU1MThg0bhpUrV8Jo5O+SUJA6zDuihKC/UjYXEB0+PZdz90TuvKayxWJBSUkJPvjgA0RHR2PGjBkYPnw4+vXr53rOokWL8Pzzz2PIkCFYsmQJtmzZguzsbFkLP9lwGscvfo3+8X3Rp0ey39t1jeqKJlsT+sf3BQAcv/g1fqpLQTxMbs/fU/NPVJ39J5pszbjccgUGnR539/wJbu2aiP7xfXHAehCfn/8XukZ1RWdjZ5xrtKDZcRU66BFtiIJdsMMhChAhQg8dBIiSjoPc5Ax5h+UErn/xERznjgK2ZueDoiDJvm+E/e4varD1bydx+arN6zacvye18xr4VVVVSEtLQ1xcHAAgIyMDFRUVeOqppwAANTU1uHbtGoYMGQIAmDJlCtatWydr4J9sOI11+0thF+ww6o3IGzrPp9C/sZ1NcP7w66CDXqeHDjo4RAcqTn+Kp4f8sK89Nf/Eu0f/3GY/n1v2u7YXvw/wSy2X3Z4jQsA1x3W3xyIl7LdMXw+rVd5TFh2WE7i6vcjnbt0frcP+7Yqjku+fKFJ5Dfza2lqYTD90vWazGQcOHGh3vclkgsVi8auIhIRufj1/j/U7OAQ7RIhwiA6cbfkOw013+7zdDSJECN933wBgF9z3dfDgoQ73J0ZIgHuzZfr6No+ZTLGyvubFY9/gqgxh36fwh1/QX52s92tbT+9Z7nGIFBwHp0gfB6+BLwgCdDqda1kURbdlb+t9ceFCIwTB9/DsFd0bBr0REOww6AzoFd3bp470xnaiYIMI9w5fEB0w6t33NSjuLhywHG53f607/EjhaYrm5rEzmWLl7/B73AnoDJJ1+De6+tZ1p/S5BfuPWX3a/s2CsWEZh0jAcXBS0jjo9Tq/G2XAh8BPSkrCvn37XMtWqxVms9ltvdX6ww9VXV2d23o59OmRjLyh8/yew2+9ncc5/DtTEC/+8NfKyNuGA0DEzOEr4aCqrwyJ/RBz/7NBzeF7Oyj7b0NuAwCvc/icuyet0Imi2GECWSwWzJw5E++//z66dOmCGTNmYNWqVUhNTXU9Z9KkSVi5ciXuueceLFu2DMnJyXjsscd8LsLfDl8uSvoNHk4cByeOgxPHwUlJ4xBoh+/1G68SExORn5+PnJwcPPDAA5g0aRJSU1ORm5uLr776CgCwdu1aFBUV4b777sPVq1eRk5Pj/zsgIiJZee3wQ4EdvrJwHJw4Dk4cBycljYNsHT4REakDA5+ISCMY+EREGqGIG97o9f6dty8nJdUSThwHJ46DE8fBSSnjEGgdijhoS0RE8uOUDhGRRjDwiYg0goFPRKQRDHwiIo1g4BMRaQQDn4hIIxj4REQawcAnItIIBj4RkUZoPvCrq6sxdepUTJ48GbNnz0ZNTQ0A4PLly5g3bx4yMzMxa9Yst2/1UrPy8nJMmDAB48ePx8aNG8NdTsi8+uqrmDhxIiZOnIgXX3R+c1hVVRWysrIwfvx4lJSUhLnC0HrhhRdQUFAAADh8+DCmTJmCjIwMFBYWwm63e9laHXbt2oUpU6YgMzMTzz//PAAVfCZEjRszZox4+PBhURRF8b333hPnz58viqIorly5Unz99ddFURTFDz/8UFy4cGHYagyV8+fPi2PGjBEvXrwoNjU1iVlZWeLx48fDXZbs/vGPf4jTp08Xr1+/Lra0tIg5OTlieXm5OHr0aPHMmTOizWYT58yZI+7evTvcpYZEVVWVOHz4cPGZZ54RRVEUJ06cKO7fv18URVF89tlnxY0bN4azvJA4c+aMOHLkSPHcuXNiS0uLOHPmTHH37t0R/5nQdIff0tKChQsXYuDAgQCAAQMG4Ny5cwCA3bt3IysrC4DzKxz/9re/wWZr/3tR1aCqqgppaWmIi4tDTEwMMjIyUFFREe6yZGcymVBQUIDo6GhERUWhb9++OHXqFJKTk3FYhfmBAAADVUlEQVT77bfDaDQiKytLE2Nx6dIllJSUYP78+QCAmpoaXLt2DUOGDAEATJkyRRPj8Mknn2DChAlISkpCVFQUSkpK0KVLl4j/TGg68KOjozF58mQAgCAIePXVVzFu3DgAQG1tLUwm5xeaG41GdOvWDfX19WGrNRRav2cAMJvNsFgsYawoNPr37+8KtFOnTuHjjz+GTqfT5FgsX74c+fn56N69O4C2nwmTyaSJcTh9+jQcDgfmz5+PyZMnY9OmTar4+VDE7ZFD4eOPP0ZRUZHbY3369MGGDRvQ0tKCgoIC2O12PP744x63F0URer26fz8KggCd7ofbroqi6LasdsePH8fjjz+OxYsXw2Aw4NSpU651WhiL9957D7feeitGjBiBDz74AIB2PxMOhwP79u3Dn/70J8TExGDBggXo3LlzxI+FZgI/MzMTmZmZbR5vamrCggULEBcXh/Xr1yMqKgqA87d3XV0dkpKSYLfb0dTUhLi4uFCXHVJJSUnYt2+fa9lqtcJsNoexotCprq5GXl4elixZgokTJ+Kzzz5zO1CvhbH46KOPYLVaMXnyZDQ0NODq1avQ6XRu41BXV6f6cQCAnj17YsSIEbjlllsAAOPGjUNFRQUMBoPrOZH4mVB3y+qDRYsWITk5GS+//DKio6Ndj48ePRpbt24F4PxBGDZsmOuXgVqlp6dj7969qK+vR3NzMyorKzFq1KhwlyW7c+fO4cknn8TatWsxceJEAMDgwYPxzTffuP6037Fjh+rH4q233sKOHTuwbds25OXlYezYsSgqKkKnTp1QXV0NANi2bZvqxwEAxowZgz179uDy5ctwOBz4+9//jvvuuy/iPxOa6fA9OXToED799FP069cPDz74IABnZ19WVoaFCxeioKAAEydORGxsLNauXRvmauWXmJiI/Px85OTkwGazYerUqUhNTQ13WbJ74403cP36dRQXF7semzFjBoqLi/H000/j+vXrGD16NO67774wVhk+a9euxdKlS9HY2IhBgwYhJycn3CXJbvDgwXjssceQnZ0Nm82Gn/3sZ5g5cyb69OkT0Z8JfuMVEZFGaH5Kh4hIKxj4REQawcAnItIIBj4RkUYw8ImINIKBT0SkEQx8IiKNYOATEWnE/wetuNWyqk3RBgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Use your ecdf() function to generate x and y values for CDFs\n",
    "x_std1, y_std1 = ecdf(sample_std1)\n",
    "x_std3, y_std3 = ecdf(sample_std3)\n",
    "x_std10, y_std10 = ecdf(sample_std10)\n",
    "#Plot all three CDFs\n",
    "sns.set()\n",
    "_ = plt.plot(x_std1, y_std1, marker= '.', linestyle='none')\n",
    "_ = plt.plot(x_std3, y_std3, marker= '.', linestyle='none')\n",
    "_ = plt.plot(x_std10, y_std10, marker= '.', linestyle='none')\n",
    "\n",
    "_ = plt.legend(('std = 1', 'std = 3', 'std = 10'))\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Are the Belmont Stakes results Normally distributed?\n",
    "Since 1926, the Belmont Stakes is a 1.5 mile-long race of 3-year old thoroughbred horses. Secretariat ran the `fastest Belmont Stakes in history in 1973`. While that was the fastest year, `1970 was the slowest` because of unusually wet and sloppy conditions. With these two outliers removed from the data set, compute the mean and standard deviation of the Belmont winners' times. Sample out of a Normal distribution with this mean and standard deviation using the np.random.normal() function and plot a CDF. Overlay the ECDF from the winning Belmont times. Are these close to Normally distributed?\n",
    "\n",
    "Note: Justin scraped the data concerning the Belmont Stakes from the Belmont Wikipedia page.\n",
    "\n",
    "   #### Instructions\n",
    "\n",
    "    1- Compute mean and standard deviation of Belmont winners' times with the two outliers removed. The NumPy array belmont_no_outliers has these data.\n",
    "\n",
    "    2- Take 10,000 samples out of a normal distribution with this mean and standard deviation using np.random.normal().\n",
    "\n",
    "    3- Compute the CDF of the theoretical samples and the ECDF of the Belmont winners' data, assigning the results to x_theor, y_theor and x, y, respectively.\n",
    "\n",
    "    4-Hit submit to plot the CDF of your samples with the ECDF, label your axes and show the plot."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 254,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "   Year            Winner           Jockey             Trainer  \\\n",
      "0  2016           Creator   Irad Ortiz, Jr      Steve Asmussen   \n",
      "1  2015  American Pharoah  Victor Espinoza         Bob Baffert   \n",
      "2  2014          Tonalist     Joel Rosario  Christophe Clement   \n",
      "3  2013     Palace Malice       Mike Smith       Todd Pletcher   \n",
      "4  2012        Union Rags   John Velazquez        Michael Matz   \n",
      "\n",
      "                Owner     Time    Track  miles  \n",
      "0    WinStar Farm LLC  2:28.51  Belmont    1.5  \n",
      "1  Zayat Stables, LLC  2:26.65  Belmont    1.5  \n",
      "2     Robert S. Evans  2:28.52  Belmont    1.5  \n",
      "3      Dogwood Stable  2:30.70  Belmont    1.5  \n",
      "4    Phyllis M. Wyeth  2:30.42  Belmont    1.5  \n"
     ]
    }
   ],
   "source": [
    "belmont = pd.read_csv('data/belmont.csv')\n",
    "print(belmont.head())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 265,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "144.0 154.0\n"
     ]
    }
   ],
   "source": [
    "time = pd.DatetimeIndex(belmont['Time'])\n",
    "belmont['Time_minute'] = time.hour*60 + time.minute + time.second /60\n",
    "belmont['Time_minute'] =round(belmont['Time_minute'],2)\n",
    "belmont_outliers = belmont['Time_minute']\n",
    "print(min(belmont_outliers), max(belmont_outliers))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 266,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "146.0 153.2\n"
     ]
    }
   ],
   "source": [
    "#let's get read of these min and max (outliers) value\n",
    "belmont_no_outliers = np.sort(belmont_outliers)[1:-1]\n",
    "print(min(belmont_no_outliers), max(belmont_no_outliers))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 267,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "149.21955056179777 1.6192389043825421\n"
     ]
    }
   ],
   "source": [
    "#Compute mean and standard deviation of Belmont winners' times \n",
    "mu = np.mean(belmont_no_outliers)\n",
    "sigma = np.std(belmont_no_outliers)\n",
    "print(mu, sigma)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 268,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Take 10,000 samples out of a normal distribution with this mean and standard deviation\n",
    "b_sample = np.random.normal(mu, sigma, size=10000)\n",
    "\n",
    "b_x, b_y = ecdf(belmont_no_outliers)\n",
    "bx_theory, by_theoty = ecdf(b_sample)\n",
    "\n",
    "_ = plt.plot(bx_theory, by_theoty,color='red')\n",
    "_ = plt.plot(b_x, b_y, marker='.', linestyle='none')\n",
    "_ = plt.xlabel('Belmont winning time (sec.)')\n",
    "_ = plt.ylabel('C D F')\n",
    "\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "What are the chances of a horse matching or beating Secretariat's record?\n",
    "Assume that the Belmont winners' times are Normally distributed (with the 1970 and 1973 years removed), what is the probability that the winner of a given Belmont Stakes will run it as fast or faster than Secretariat?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 269,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Probability of besting Secretariat: 0.000651\n"
     ]
    }
   ],
   "source": [
    "#Take 1,000,000 samples from the normal distributio\n",
    "samp  = np.random.normal(mu, sigma, size= 1000000)\n",
    "#Compute the fraction of samples that have a time less than or equal to \n",
    "#Secretariat's time of 144 seconds\n",
    "prob = sum(samp <=144)/1000000\n",
    "print('Probability of besting Secretariat:', prob)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Exponential distrubition\n",
    "\n",
    "The waiting time between arrvials of a Poisson process is Exponentially distrubuted. The Exponential distrubition has a single parameter which is mean of waiting time. And the Exponential distrubition don't have a peak."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### If you have a story, you can simulate it!\n",
    "Sometimes, the story describing our probability distribution does not have a named distribution to go along with it. In these cases, fear not! You can always simulate it. We'll do that in this and the next exercise.\n",
    "\n",
    "In earlier exercises, we looked at the rare event of no-hitters in Major League Baseball. Hitting the cycle is another rare baseball event. When a batter hits the cycle, he gets all four kinds of hits, a single, double, triple, and home run, in a single game. Like no-hitters, this can be modeled as a Poisson process, so the time between hits of the cycle are also Exponentially distributed.\n",
    "\n",
    "How long must we wait to see both a no-hitter and then a batter hit the cycle? The idea is that we have to wait some time for the no-hitter, and then after the no-hitter, we have to wait for hitting the cycle. Stated another way, what is the total waiting time for the arrival of two different Poisson processes? The total waiting time is the time waited for the no-hitter, plus the time waited for the hitting the cycle.\n",
    "\n",
    "Now, you will write a function to sample out of the distribution described by this story."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 274,
   "metadata": {},
   "outputs": [],
   "source": [
    "def successive_poisson(tau1, tau2, size=1):\n",
    "    \"\"\"Define a function with call signature successive_poisson(tau1, tau2, size=1) \n",
    "    that samples the waiting time for a no-hitter and a hit of the cycle\"\"\"\n",
    "    t1 = np.random.exponential(tau1, size)\n",
    "    t2 = np.random.exponential(tau2, size)\n",
    "    #The function returns the sum of the waiting times for the two events\n",
    "    return t1+t2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Distribution of no-hitters and cycles\n",
    "Now, you'll use your sampling function to compute the waiting time to observe a no-hitter and hitting of the cycle. The mean waiting time for a no-hitter is 764 games, and the mean waiting time for hitting the cycle is 715 games.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 275,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Use your successive_poisson() function to draw 100,000 out of the distribution of waitin\n",
    "waiting_times = successive_poisson(764, 715, size=100000)\n",
    "#Plot the PDF of the waiting times using the step histogram technique\n",
    "_ = plt.hist(waiting_times, bins=100, histtype='step')\n",
    "\n",
    "_ = plt.xlabel('X')\n",
    "_ = plt.ylabel('Y')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 281,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_wait = np.mean(waiting_times)\n",
    "sample_wait = np.random.exponential(mean_wait, size=10000)\n",
    "x_wait, y_wait = ecdf(waiting_times)\n",
    "x_the, y_the =ecdf(sample_wait)\n",
    "_ = plt.plot(x_wait, y_wait)\n",
    "_ = plt.plot(x_the, y_the)\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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