{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "tags": [
     "remove-input"
    ]
   },
   "outputs": [],
   "source": [
    "# Install datascience package if needed\n",
    "try:\n",
    "    import datascience\n",
    "except ImportError:\n",
    "    import micropip\n",
    "    await micropip.install('datascience')\n",
    "from datascience import *\n",
    "path_data = '../../../assets/data/'\n",
    "import matplotlib\n",
    "matplotlib.use('Agg')\n",
    "%matplotlib inline\n",
    "import matplotlib.pyplot as plots\n",
    "plots.style.use('fivethirtyeight')\n",
    "import numpy as np"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Sampling from a Population\n",
    "\n",
    "The law of averages also holds when the random sample is drawn from individuals in a large population.\n",
    "\n",
    "As an example, we will study a population of flight delay times. The table `united` contains data for United Airlines domestic flights departing from San Francisco in the summer of 2015. The data are made publicly available by the [Bureau of Transportation Statistics](http://www.transtats.bts.gov/Fields.asp?Table_ID=293) in the United States Department of Transportation.\n",
    "\n",
    "There are 13,825 rows, each corresponding to a flight. The columns are the date of the flight, the flight number, the destination airport code, and the departure delay time in minutes. Some delay times are negative: those flights left early."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<table border=\"1\" class=\"dataframe\">\n",
       "    <thead>\n",
       "        <tr>\n",
       "            <th>Date</th> <th>Flight Number</th> <th>Destination</th> <th>Delay</th>\n",
       "        </tr>\n",
       "    </thead>\n",
       "    <tbody>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>73           </td> <td>HNL        </td> <td>257  </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>217          </td> <td>EWR        </td> <td>28   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>237          </td> <td>STL        </td> <td>-3   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>250          </td> <td>SAN        </td> <td>0    </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>267          </td> <td>PHL        </td> <td>64   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>273          </td> <td>SEA        </td> <td>-6   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>278          </td> <td>SEA        </td> <td>-8   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>292          </td> <td>EWR        </td> <td>12   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>300          </td> <td>HNL        </td> <td>20   </td>\n",
       "        </tr>\n",
       "        <tr>\n",
       "            <td>6/1/15</td> <td>317          </td> <td>IND        </td> <td>-10  </td>\n",
       "        </tr>\n",
       "    </tbody>\n",
       "</table>\n",
       "<p>... (13815 rows omitted)</p>"
      ],
      "text/plain": [
       "Date   | Flight Number | Destination | Delay\n",
       "6/1/15 | 73            | HNL         | 257\n",
       "6/1/15 | 217           | EWR         | 28\n",
       "6/1/15 | 237           | STL         | -3\n",
       "6/1/15 | 250           | SAN         | 0\n",
       "6/1/15 | 267           | PHL         | 64\n",
       "6/1/15 | 273           | SEA         | -6\n",
       "6/1/15 | 278           | SEA         | -8\n",
       "6/1/15 | 292           | EWR         | 12\n",
       "6/1/15 | 300           | HNL         | 20\n",
       "6/1/15 | 317           | IND         | -10\n",
       "... (13815 rows omitted)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united = Table.read_table(path_data + 'united_summer2015.csv')\n",
    "united"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "One flight departed 16 minutes early, and one was 580 minutes late. The other delay times were almost all between -10 minutes and 200 minutes, as the histogram below shows."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-16"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united.column('Delay').min()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "580"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united.column('Delay').max()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delay_bins = np.append(np.arange(-20, 301, 10), 600)\n",
    "united.hist('Delay', bins = delay_bins, unit = 'minute')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the purposes of this section, it is enough to zoom in on the bulk of the data and ignore the 0.8% of flights that had delays of more than 200 minutes. This restriction is just for visual convenience; the table still retains all the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.008390596745027125"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united.where('Delay', are.above(200)).num_rows/united.num_rows"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delay_bins = np.arange(-20, 201, 10)\n",
    "united.hist('Delay', bins = delay_bins, unit = 'minute')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The height of the [0, 10) bar is just under 3% per minute, which means that just under 30% of the flights had delays between 0 and 10 minutes. That is confirmed by counting rows: "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.2935985533453888"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "united.where('Delay', are.between(0, 10)).num_rows/united.num_rows"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Empirical Distribution of the Sample\n",
    "\n",
    "Let us now think of the 13,825 flights as a population, and draw random samples from it with replacement. It is helpful to package our code into a function. The function `empirical_hist_delay` takes the sample size as its argument and draws an empiricial histogram of the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def empirical_hist_delay(n):\n",
    "    united.sample(n).hist('Delay', bins = delay_bins, unit = 'minute')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "As we saw with the dice, as the sample size increases, the empirical histogram of the sample more closely resembles the histogram of the population. Compare these histograms to the population histogram above."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(10)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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tt01qamoTVlRTsaQMEolE4f6N6VssKVbrZ1en1vq5G4NzphjOm2IaM29isbjedYJDraioCJMmTcKtW7dgaGgIiUSCRYsWAQDat2+PtWvXYvr06Vi/fr3ChcprzZo1SExMxLlz56CtrV1vO1kToGr3fsmAgYGBwv0b09fQwBBicXeF+7dUqampav2dt0ScM8Vw3hSjynkTvPvR398fDx48wMmTJ5GcnAypVFq9TltbG+PHj8eFCxdUUmRdVq9ejejoaMTGxqJHjx5NNi4RETVfgkPtzJkzmD9/PkaNGlXnWY7W1tbIzMxUanH1WbVqFaKiohAbG4s33nijScYkIqLmT/Dux8LCQvTs2bPe9VKpFGVlZUopSpbly5fjxIkTOHbsGIyMjJCTkwPg9W46Q0NDlY9PRETNl+AttW7duuH+/fv1rr969SpsbGyUUpQsoaGheP78OTw8PNC7d+/qn927d6t8bCIiat4Eb6lNnToVO3bswPjx49G3b18A/3ex9f79+3H69Gl89tlnqqnyTwoLC1U+BhERtUyCQ+3jjz/GDz/8gAkTJsDGxgYikQi+vr7Iz89HTk4Oxo0bhwULFqiyViIiIpkEh1qbNm0QGRmJkydP4tSpUxCJRCgvL4eTkxMmTZqEadOmNcltsoiIiOoj18XXwOvdkFOnTlVFLURERI0id6gBwI8//lh9+r6VlRXs7Oy4lUZERGonV6hFR0djw4YN+O2336ovvhaJRLCwsMCGDRu4BUdERGolONQiIiLwwQcfQCwWw9/fHzY2NpBKpfj1119x5MgRLFiwAGVlZfD29lZlvURERPUSHGrbtm2Di4sLTp8+DX19/Rrr5s2bh7Fjx2Lbtm0MNSIiUhvBF18/efIEU6dOrRVoAKCvrw9PT0/89ttvSi2OiIhIHoJDrU+fPvj999/rXf/bb7+hd+/eSimKiIhIEYJD7dNPP0V4eDi++uqrWuuio6Nx5MgRbNy4UanFERERyUPwMbXdu3ejU6dOmDNnDnx9fdGzZ0+IRCI8evQIubm5sLa2xq5du7Br167qPiKRCJGRkSopnIiI6K8Eh9qDBw8gEolgaWkJANXHz/T09GBpaYnS0lL8/PPPNfrw2jUiImpKgkMtJSVFlXUQERE1muBjakRERM0dQ42IiDQGQ42IiDQGQ42IiDQGQ42IiDQGQ42IiDSG4FBzcnJCfHx8vevPnTsHJycnpRRFRESkCMGh9vjxY0gkknrXSySS6geHCnX16lVMnz4dffv2hZGRESIiImS2z8jIgJGRUa2fixcvyjUuERFpJrkeEirrDiEPHz5E+/bt5RpcIpHA1tYWM2bMwMKFCwX3i46Ohr29ffVrY2NjucYlIiLNJDPUjh8/ji+++KL6dXBwMMLDw2u1KywsxP379zFmzBi5Bnd3d4e7uzsAYNGiRYL7mZiYwNzcXK6xiIhI88kMNYlEgpycnOrXRUVFqKysrNFGJBKhXbt2eO+99+Dr66uaKv9i5syZKCkpgbW1NRYtWgQPD48mGZeIiJo3maE2b948zJs3DwDg6OiILVu2YOzYsU1SWF0MDQ2xceNGDBo0CDo6OoiPj4ePjw9CQkLg6elZb7/U1NQmrLKmYkmZzGORDWlM32JJsVo/uzq11s/dGJwzxXDeFNOYeROLxfWuE3xM7e7duwoXoCydOnXCkiVLql/369cP+fn52Llzp8xQkzUBqnbvlwwYGBgo3L8xfQ0NDCEWd1e4f0uVmpqq1t95S8Q5UwznTTGqnDe5ThQBgOfPnyMrKwsFBQWQSqW11g8ZMkQphQnl4uLS4FmTRETUOggOtYKCAqxatQpfffUVKioqaq2XSqUQiUTIz89XaoENSUlJ4UkjREQEQI5Q+/jjj3H69GnMmzcPQ4YMgZGRUaMHLy4uxqNHjwAAlZWVyMrKwt27d2FsbAwrKyv4+/sjKSkJsbGxAF6fjdmmTRs4OjpCS0sL586dQ2hoKPz8/BpdiyYSiV7v/lSEqXEHmJvxUgkialkEh9rFixexYMECbN68WWmD3759G+PHj69+HRAQgICAAMyYMQMhISHIzs5GWlpajT7BwcHIzMyEtrY2rK2tsWfPHpnH01qzoucvsCPsK4X6rl/qzVAjohZHcKjp6urC2tpaqYMPHToUhYWF9a4PCQmp8drLywteXl5KrYGIiDSH4NtkeXh44MKFC6qshYiIqFEEh9qSJUuQnZ2NhQsX4ubNm8jOzkZubm6tHyIiInURvPvRxcUFIpEIycnJiIyMrLddU5/9SEREVEVwqK1cuVLmDY2JiIjUTXCorV69WpV1EBERNZpCT76uqKhAfn4+ysvLlV0PERGRwuQKtVu3bmHixImwsLCAjY0Nrl69CgDIy8vDtGnT8N1336mkSCIiIiEEh9r333+PsWPHIi0tDdOnT69x38dOnTqhuLgYR48eVUmRREREQggOtY0bN8La2ho3btzA+vXra60fOnQofvjhB6UWR0REJA/BoXbr1i3885//hL6+fp1nQXbt2rXGA0WJiIiamuBQ09LSgpZW/c1zcnLQtm1bpRRFRESkCMGh5uzsjHPnztW5rqysDCdPnoSrq6vSCiMiIpKX4FD75JNPcPnyZXzwwQdISUkBAGRnZ+PixYuYMGEC0tLSsGzZMpUVSkRE1BDBF1+PGDEC+/fvx4oVK3D8+HEAwPvvvw+pVIqOHTsiNDQUAwYMUFmhREREDREcagAwZcoUjB07FpcuXcKvv/6KyspK9OzZE25ubjA0NFRVjURERILIFWoA0K5dO4wbN04VtRARETWK4GNq8fHxWLFiRb3rV6xYUe+JJERERE1BcKjt3r0bL168qHd9SUkJdu7cqZSiiIiIFCE41O7fvw9nZ+d61zs5OeHBgwdKKYqIiEgRgkOtvLwcL1++rHf9y5cvUVpaqpSiiIiIFCE41GxtbREbG4vKyspa6yorKxEbG4s+ffootbi6XL16FdOnT0ffvn1hZGSEiIgIlY9JREQtg+BQW7hwIZKSkjBjxgwkJyejtLQUpaWlSE5OhpeXF5KSkrBgwQJV1goAkEgksLW1xZYtW3hbLiIiqkHwKf2TJ09GWloaAgICcOHCBQCASCSCVCqFSCTCqlWr4OnpqbJCq7i7u8Pd3R0AsGjRIpWPR0RELYdc16ktX74cU6ZMQVxcHNLT0yGVStGzZ0+MHz8ePXr0UFGJREREwggKtdLSUsTExOCNN96Ai4sLlixZouq6lCo1NVVtYxdLyiCRSBTu35i+5RXlCvcvlhSrdd4aqyXXri6cM8Vw3hTTmHkTi8X1rhMUanp6evjwww+xdetWuLi4KFyIusiaAFW790sGDAwMFO7fmL462joK9zc0MIRY3F3hsdUpNTVVrb/zlohzphjOm2JUOW+CTxQRi8V8CCgRETVrgkNt5cqVOHDgAO7du6fKeoiIiBQm+ESRy5cvw8zMDMOGDYOrqyt69uxZ65R6kUiE4OBgpRf5Z8XFxXj06BGA19fHZWVl4e7duzA2NoaVlZVKxyYiouZNcKiFhYVV/zkxMRGJiYm12jRFqN2+fRvjx4+vfh0QEICAgADMmDEDISEhKh2biIiaN8GhVlBQoMo6BBs6dCgKCwvVXQYRETVDgo+pERERNXdyPyQ0MTERly9fRm5uLhYsWAAbGxtIJBI8ePAAYrEYHTp0UEWdREREDRIcamVlZZg9ezbi4+Orb431X//1X7CxsYG2tjamTJmCxYsXY/ny5aqsl4iIqF6Cdz8GBATg/PnzCAoKws2bNyGVSqvX6evrY+LEiTh79qxKiiQiIhJCcKidPHkSs2bNwpw5c2BiYlJrvVgsRnp6ujJrIyIikovgUMvNzYWDg0O96/X09Bp1n0IiIqLGEhxq5ubmMrfEkpKS0L17y7xXIBERaQbBoTZhwgQcOnQIDx8+rF4mEokAAGfPnsXJkycxadIk5VdIREQkkOBQW7VqFaysrDB8+HDMnTsXIpEI27Ztw6hRo+Dt7Q1nZ2d8+OGHqqyViIhIJsGh1r59e/znP//BJ598gtzcXOjr6yMxMRESiQSrV69GXFwc9PX1VVkrERGRTHJdfK2vr49ly5Zh2bJlqqqHiIhIYQ2GWmlpKeLj45Geng4TExOMGTMGnTt3boraiIiI5CIz1HJycjB27FikpaVVX2zdrl07REZGYsiQIU1SIBERkVAyj6lt2rQJ6enpWLRoEU6cOIGAgADo6+tj5cqVTVUfERGRYDK31L755hvMmDEDmzZtql72t7/9DXPnzsWTJ0/QtWtXlRdIREQklMwttZycHAwcOLDGskGDBkEqlSIrK0ulhREREclLZqhVVFTUOk2/6nVJSYnqqiIiIlJAg2c/pqenIykpqfr1H3/8AQBITU2FoaFhrfYuLi5KLI+IiEi4BkMtICAAAQEBtZb/9WSRqmes5efnK686IiIiOcgMtb179zZVHURERI0mM9S8vLxUXkBoaCh27dqFnJwc9OnTBwEBARg8eHCdbTMyMuDk5FRreVRUFEaNGqXqUomIqJmT6zZZyhYTEwNfX198/vnnGDRoEEJDQzF16lQkJibCysqq3n7R0dGwt7evfm1sbNwU5RIRUTMn+IbGqrB37154eXnhvffeQ+/evREUFARzc3OEhYXJ7GdiYgJzc/PqH11d3SaqmIiImjO1hVpZWRmSk5MxcuTIGstHjhyJGzduyOw7c+ZM2NjYYMyYMfj6669VWSYREbUgatv9mJeXh4qKCpiZmdVYbmZmhqdPn9bZx9DQEBs3bsSgQYOgo6OD+Ph4+Pj4ICQkBJ6envWOlZqaqtTa5VEsKYNEIlG4f2P6lleUK9y/vPwVbty+p/DYHQ0NUVRcrFBfI8N20EK5wmMD6v2dt1ScM8Vw3hTTmHkTi8X1rlPrMTXg/56eXaXq0oC6dOrUCUuWLKl+3a9fP+Tn52Pnzp0yQ03WBKjavV8yYGBgoHD/xvTV0dZRuP+LklfYEab4VvBHs99VuP/6pd6we0Px31lqaqpaf+ctEedMMZw3xahy3tS2+7FTp07Q1tautVX27NmzWltvsri4uODRo0fKLo+IiFogtYWarq4unJ2dcenSpRrLL126VOt+k7KkpKTA3Nxc2eUREVELpNbdj4sXL8aCBQvg4uKCgQMHIiwsDNnZ2fDx8QEA+Pv7IykpCbGxsQCA48ePo02bNnB0dISWlhbOnTuH0NBQ+Pn5qfFTEBFRc6HWUJs0aRLy8/MRFBSEnJwc9O3bF5GRkejWrRsAIDs7G2lpaTX6BAcHIzMzE9ra2rC2tsaePXtkHk8jIqLWQ+0nisydOxdz586tc11ISEiN115eXk1ylxNSL5Ho9Qk2itIRqf1rTURqwr/91OwUPX+BHWFfKdz/kzkeSqyGiFoStd5RhIiISJkYakREpDEYakREpDEYakREpDEYakREpDEYakREpDEYakREpDEYakREpDEYakREpDEYakREpDEYakREpDF470fSOPp6egrfELmdvh5elJQqPLapcQeYmxkr1DcntwDPCv5Qy9iV0GnUTaQbMzaRMjHUSOP8IXmJPeGRCvX9aPa7jbqZ8vql3gr/4/6s4A98uitCLWMXFr/AtoNfq2VsImXi7kciItIYDDUiItIYDDUiItIYDDUiItIYPFGESIlEIih8FmFpWZnaxgZEjRqbqLlgqBEpUdHzFwqfPfnR7HfVNvYH741v1NhEzUWL3P0YGhoKR0dHmJubY/jw4bh27Zq6SyIiomagxYVaTEwMfH19sWzZMly+fBmurq6YOnUqMjMz1V0aERGpWYsLtb1798LLywvvvfceevfujaCgIJibmyMsLEzdpRERkZqJCgsLpeouQqiysjJ06dIFBw8exMSJE6uXL1++HPfv30d8fLwaqyMiInVrUVtqeXl5qKiogJmZWY3lZmZmePr0qZqqIiKi5qJFhVoVkajm6cdSqbTWMiIian1aVKh16tQJ2tratbbKnj17VmvrjYiIWp8WFWq6urpwdnbGpUuXaiy/dOkSBg4cqKaqiIiouWhxF18vXrwYCxYsgIuLCwYOHIiwsDBkZ2fDx8dH3aUREZGatagtNQCYNGkSAgICEBQUhKFDhyIxMRGRkXJ/dJ8AAA2mSURBVJHo1q2buktTKl5gXr+AgAAYGRnV+HnjjTeq10ulUgQEBKBPnz7o3Lkzxo0bh59++kmNFavH1atXMX36dPTt2xdGRkaIiKj5rDYh81RaWooVK1agV69esLCwwPTp0/HkyZOm/BhNqqE5e//992t990aNGlWjTWubs23btmHEiBGwsrKCtbU1PD09cf/+/RptmvK71uJCDQDmzp2LlJQUPH36FN999x2GDBmi7pKUiheYN0wsFuPnn3+u/vlz6O/cuRN79+5FYGAgvvnmG5iZmeHdd9/F8+fP1Vhx05NIJLC1tcWWLVvQtm3bWuuFzNPq1asRFxeHgwcPIj4+Hs+fP4enpycqKiqa8qM0mYbmDADefvvtGt+9kydP1ljf2uYsISEBc+bMwfnz5xEbGwsdHR1MnDgRBQUF1W2a8rvWoq5Tay3c3NxgZ2eHXbt2VS9788034eHhgQ0bNqixsuYhICAAsbGxuH79eq11UqkUffr0wbx587B8+XIAwMuXLyEWi7Fx48ZWu5u6a9eu2Lp1K7y9vQEIm6eioiLY2Nhg7969mDZtGgAgKysLDg4OiIqKgpubm9o+T1P465wBr7fU8vPzceLEiTr7tPY5A4Di4mJ069YNEREReOedd5r8u9Yit9Q0WVlZGZKTkzFy5Mgay0eOHIkbN26oqarmJz09HX379oWjoyNmz56N9PR0AEBGRgZycnJqzF/btm0xePBgzt+fCJmn5ORkvHr1qkYbS0tL9O7du1XP5fXr12FjYwMXFxcsXboUubm51es4Z69DrbKyEkZGRgCa/rvW4k4U0XS8wLxh/fv3x759+yAWi/Hs2TMEBQXB3d0diYmJyMnJAYA65+/3339XR7nNkpB5evr0KbS1tdGpU6dabVrrd3HUqFEYP348unfvjsePH2PTpk2YMGECvv32W+jp6XHOAPj6+sLBwQGurq4Amv67xlBrpniBef1Gjx5d43X//v3h7OyM48ePY8CAAQA4f0IpMk+teS4nT55c/Wc7Ozs4OzvDwcEB58+fx4QJE+rt11rmbM2aNUhMTMS5c+egra1dY11Tfde4+7GZ4QXm8jM0NESfPn3w6NEjmJubAwDnrwFC5ulvf/sbKioqkJeXV2+b1q5Lly6wsLDAo0ePALTuOVu9ejWio6MRGxuLHj16VC9v6u8aQ62Z4QXm8ispKUFqairMzc3RvXt3mJub15i/kpISXL9+nfP3J0LmydnZGW3atKnR5smTJ/j55585l/9fXl4efv/99+p/uFvrnK1atQpRUVGIjY2tcXkN0PTfNW1fX18/xT8KqUL79u0REBCAzp07Q19fH0FBQbh27Rr27NmDjh07qrs8tfuf//kf6OrqorKyEg8fPsSKFSvw6NEjbN++HUZGRqioqMD27dthY2ODiooKrF27Fjk5OdixYwf09PTUXX6TKS4uxoMHD5CTk4OjR4/C1tYWHTp0QFlZGTp27NjgPOnr6yM7OxsHDhyAvb09ioqK8PHHH6NDhw7w9/eHlpbm/Z9Y1pxpa2vj008/haGhIcrLy5GSkoIlS5agoqICQUFBrXbOli9fji+//BKHDx+GpaUlJBIJJBIJgNf/SReJRE36XeMp/c1UaGgodu7ciZycHPTt2xefffaZxl2Pp6jZs2fj2rVryMvLg6mpKfr374+1a9eiT58+AF7vh9+yZQsOHz6MwsJCuLi4IDg4GLa2tmquvGlduXIF48ePr7V8xowZCAkJETRPJSUlWLduHaKiolBSUoJhw4bh888/h6WlZVN+lCYja862bdsGb29v3L17F0VFRTA3N8fQoUOxdu3aGvPR2uas6izHv1q1ahVWr14NQNjfSWXNG0ONiIg0huZtCxMRUavFUCMiIo3BUCMiIo3BUCMiIo3BUCMiIo3BUCMiIo3BUCONFhERUeOBjhYWFnBwcIC3tze++uorVFZWKvS+V65cgZGREa5cuaLkihv29ddfQywW48WLF0p5v6o5ysjIUMr71eXKlSsICAhQeL7v3LmDLl268JmC1CCGGrUK4eHhuHDhAiIjI7F27Vro6elhzpw5ePfdd/Hy5Ut1lydYeXk5Nm7ciKVLl6Jdu3ZKec8xY8bgwoUL6Ny5s1Lery4JCQkIDAxUONScnJzw9ttvY/PmzUqujDQNQ41aBQcHBwwYMAB///vfMX36dISFheHQoUO4fPky1q9fr+7yBDtz5gweP36Mf/7zn0p7T1NTUwwYMKDZ30LMx8cHUVFRfIQQycRQo1bLw8MDY8eOxZEjR2rsynvx4gU2bNgAR0dHmJmZwdHREcHBwQ1uZXzzzTeYOnUqevfujS5duuCtt97C7t27azyO3tPTE8OGDavVNz09HcbGxjh06JDMMY4ePQo3NzcYGxvXWG5kZIRNmzZh9+7dsLe3h4WFBaZNm4bc3Fzk5uZi1qxZ6NatG+zs7LBjx44afeva/ejg4ID58+cjOjoarq6usLCwwNtvv13raePjxo3DuHHjatXp4OCA999/H8DrJ5UHBgYCeB2gVbuCqwid75EjR6J9+/Y4fvy4zDmi1o3PU6NWzd3dHWfOnMHt27cxZMgQlJeXY/LkyXjw4AFWrFgBOzs73Lx5E0FBQSgoKJC5+ys9PR3Dhg3D/Pnzoaenh+TkZAQGBiIvLw9+fn4AgDlz5mDatGlISkqCi4tLdd/w8HAYGBhgypQp9b5/aWkpEhISsHbt2jrXf/nll7C1tcXnn3+Op0+fYs2aNVi4cCGKi4sxatQozJo1C6dOnYKfnx9sbW3h7u4uc26uXbuG1NTU6t21mzdvhqenJ+7evVvv/f7q8t///d/47bffcPTo0VrP2ZJnvnV0dODq6oqLFy9i2bJlgsen1oWhRq1a1c1Sq57OGxUVhevXr+PMmTPVN5AePnw4ACAwMBAfffRRvc93mj17dvWfpVIpBg8ejLKyMuzevRvr16+HlpYWRo0ahR49euDQoUPVofbq1StERERg6tSpaN++fb21pqSkoKSkBPb29nWu19PTw/Hjx6Gj8/qv9U8//YR9+/Zh7dq1WLFiBQDg73//O06fPo1Tp041GGrPnz9HQkJCdYCZm5tjxIgRuHDhAqZOnSqz75917doVFhYWAF4/0LWqPkD++XZwcMDu3btRWVmpkXe8p8bjt4JaNan09f28q56u+7//+7+wsrLCwIEDUV5eXv0zcuRIvHr1Cjdv3qz3vbKzs/HRRx/B3t4eZmZmMDU1xaZNm1BUVITc3FwAgJaWFnx8fBATE4OioiIAr4+TPX36FLNmzZJZa9WxpL8+8r7KiBEjagRG1XOt3Nzcqpfp6OigV69eePLkicyxAMDV1bXGFlnVHdWzsrIa7CuUvPNtamqK0tJSFBQUKK0G0izcUqNWreof96qHPObm5iIzMxOmpqZ1ts/Pz69zeWVlJWbMmIHs7Gz4+vpCLBajbdu2OHPmDIKDg1FSUlLddubMmQgICMCJEycwf/58hIWFwcXFBU5OTjJrLS0tBYB6T+j46y7BNm3a1Lu86r1k+etxu6px//xZGkve+W7bti0AtKgzVqlpMdSoVTt//jz09fXh7OwMADAxMUH37t1x+PDhOtt369atzuVpaWm4ffs29u/fD09Pz+rlZ8+erdXWxMQEHh4eOHz4MNzc3HDlyhXs2rWrwVpNTEwAAIWFhQ22bSr6+vp4/vx5reVCa5R3vqu20OrbWiViqFGrFRsbi7Nnz2LhwoXV13y5ubkhNjYWBgYGtR5LL0vV2ZNVW0fA62NlJ0+erLP93LlzMXr0aCxZsgTt27fH5MmTGxxDLBYDeH1CiryPuFcVKysrxMbGoqysDLq6ugCAq1ev1gq6qq28ly9f1jhuKO98Z2RkwNLSsnqLjeivGGrUKqSkpCAvLw9lZWXIysrC+fPncerUKYwYMQIbNmyobjdt2jRERETAw8MDixcvhoODA8rKypCWloazZ88iIiKizouee/fuDSsrK2zcuBHa2trQ0dHBvn376q1nwIABcHJywrVr1zB//nxBF1JbWVnBysoKSUlJNbYG1WnSpEk4fPgwPvjgA3h5eSEjIwN79+5Fhw4darTr3bs3AGDPnj0YPXo0tLW10a9fP7nn+4cffsDgwYOb9DNSy8JQo1bhvffeA/B6d5mpqSmcnJwQFhYGDw+P6pNEgNdbWjExMdi+fTvCw8ORkZGBdu3aoWfPnnB3d6/eGvkrXV1dREREYOXKlVi4cCGMjY3h7e0NKysrLF26tM4+Hh4euHPnDnx8fAR/jkmTJuHUqVPYunWrHJ9edYYNG4bt27dj9+7diI2NhaOjI/79739j5syZNdr94x//wNy5c3Hw4EFs3boVUqkUhYWFcs13VlYWfvzxx3ovaSACAFFhYaFU3UUQtUZjxoyBlpZWncfd6pOWlob+/fvj9OnTeOutt1RYXfOzY8cOHDx4EMnJyTWudSP6M26pETWh0tJS3LlzB99++y1u3Lgh990xevbsCW9vb+zYsaNVhVpJSQn+9a9/YcOGDQw0komhRtSEsrOz4e7ujo4dO2LZsmUYO3as3O+xdu1aHDp0CC9evFDaTY2bu8ePH2PhwoWYPn26ukuhZo67H4mISGPwjiJERKQxGGpERKQxGGpERKQxGGpERKQxGGpERKQxGGpERKQx/h8B1j5L6PrwQAAAAABJRU5ErkJggg==",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(100)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The most consistently visible discrepancies are among the values that are rare in the population. In our example, those values are in the the right hand tail of the distribution. But as the sample size increases, even those values begin to appear in the sample in roughly the correct proportions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "empirical_hist_delay(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Convergence of the Empirical Histogram of the Sample\n",
    "What we have observed in this section can be summarized as follows:\n",
    "\n",
    "For a large random sample, the empirical histogram of the sample resembles the histogram of the population, with high probability.\n",
    "\n",
    "This justifies the use of large random samples in statistical inference. The idea is that since a large random sample is likely to resemble the population from which it is drawn, quantities computed from the values in the sample are likely to be close to the corresponding quantities in the population."
   ]
  }
 ],
 "metadata": {
  "anaconda-cloud": {},
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
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