20220409_understanding_clt_and_ttest_part1.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm, t\n",
    "import json\n",
    "import pprint"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Generating 3 arrays with uniform, random, normal distribution\n",
    "# We'll set random seed to obtain the same results if we reexecute \n",
    "# the code.\n",
    "np.random.seed(42)\n",
    "uniform_distribution = np.random.uniform(4,5.5, 1600)\n",
    "normal_distribution = np.random.normal(size = 1600, \n",
    "                                       loc = 5, \n",
    "                                       scale = 0.05)\n",
    "binomial_distribution = np.random.binomial(15,0.05,1600)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "df = pd.DataFrame(uniform_distribution, columns=['uniform'])\n",
    "df['normal'] = pd.DataFrame(normal_distribution, columns=['normal'])\n",
    "df['binomial'] = pd.DataFrame(binomial_distribution, columns=['binomial'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
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       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>uniform</th>\n",
       "      <th>normal</th>\n",
       "      <th>binomial</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>4.561810</td>\n",
       "      <td>4.970916</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5.426071</td>\n",
       "      <td>4.949262</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5.097991</td>\n",
       "      <td>4.967536</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>4.897988</td>\n",
       "      <td>4.938803</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>4.234028</td>\n",
       "      <td>5.001704</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    uniform    normal  binomial\n",
       "0  4.561810  4.970916         0\n",
       "1  5.426071  4.949262         1\n",
       "2  5.097991  4.967536         0\n",
       "3  4.897988  4.938803         1\n",
       "4  4.234028  5.001704         0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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WLX9D1cysgJzczcwKyMndzKyAnNzNzArIyd3MrICc3M3MCsjJ3cysgJzczcwKyMndzKyAnNzNzArIyd3MrICc3M3MCsjJ3cysgJzczcwKyMndzKyAnNzNzArIyd3MrIAqeYbqbpJ+I+lOSaskfT6V7y/p15JWS7pS0i6pfNc0vzrVdzU4BjMzK1HJmftm4JiIOAyYCRyXHnz9JeC8iDgQWA+ckZY/A1ifys9Ly5mZWRONmdwjM5Rmd06vAI4BrkrlFwMnp+lZaZ5Uf6wk1avBZmY2NmXPsx5jIWlHYAVwIPAN4H8Bt6ezcyRNB26IiEMl3Q0cFxFrUt2DwJER8XjJNucB8wA6OzsP7+vrqzqIoaEhOjo6ql6/HTiG8lYObmzIdkt1ToK1m5qyqzHNmDq5qvX8t9QemhFDb2/viojoHqlup0o2EBHPAzMlTQGuBl5ba6MiYjGwGKC7uzt6enqq3lZ/fz+1rN8OHEN5cxdc15Dtlpo/YwuLVlb0tmi4gdk9Va3nv6X20OoYxnW3TERsAG4G3ghMkTT8LpgGDKbpQWA6QKqfDDxRj8aamVllKrlbZp90xo6kScBbgHvJkvy702JzgGvS9LVpnlR/U1TS92NmZnVTyefPfYGLU7/7DsCSiFgq6R6gT9K/AL8HLkzLXwh8X9Jq4EnglAa028zMyhgzuUfEXcDrRyh/CDhihPLngPfUpXVmZlYVf0PVzKyAnNzNzArIyd3MrICc3M3MCsjJ3cysgNrjq3g2YXSV+abo/BlbmvZNUjMrz2fuZmYF5ORuZlZATu5mZgXk5G5mVkBO7mZmBeTkbmZWQE7uZmYF5ORuZlZATu5mZgXk5G5mVkBO7mZmBeTkbmZWQJU8IHu6pJsl3SNplaSPp/KzJQ1KuiO9Tsit8xlJqyXdL+ltjQzAzMy2VcmokFuA+RHxO0l7ACsk3ZjqzouIL+cXlnQw2UOxDwFeCfyrpFdHxPP1bLiZmY1uzDP3iHgsIn6Xpp8G7gWmllllFtAXEZsj4mFgNSM8SNvMzBpHEVH5wlIXcAtwKPBJYC7wFLCc7Ox+vaSvA7dHxKVpnQuBGyLiqpJtzQPmAXR2dh7e19dXdRBDQ0N0dHRUvX47mCgxrBzcOGpd5yRYu6mJjWmAdophxtTJVa03Uf6WynEMlent7V0REd0j1VX8sA5JHcAPgU9ExFOSLgC+AET6uQj4YKXbi4jFwGKA7u7u6OnpqXTVbfT391PL+u1gosRQ7mEc82dsYdHKif38l3aKYWB2T1XrTZS/pXIcQ+0qultG0s5kif2yiPgRQESsjYjnI+IF4Du82PUyCEzPrT4tlZmZWZNUcreMgAuBeyPiK7nyfXOLvRO4O01fC5wiaVdJ+wMHAb+pX5PNzGwslXz+PBo4DVgp6Y5U9lngVEkzybplBoAPAUTEKklLgHvI7rQ503fKmJk115jJPSJuBTRC1fVl1jkXOLeGdpmZWQ38DVUzswJycjczK6D2uOfLzLbRVea203Lmz9hS9pbVsQwsPLHqda19+MzdzKyAnNzNzArIyd3MrICc3M3MCsjJ3cysgJzczcwKyMndzKyAnNzNzArIyd3MrICc3M3MCsjJ3cysgJzczcwKyMndzKyAnNzNzAqokmeoTpd0s6R7JK2S9PFUvpekGyU9kH7umcol6WuSVku6S9IbGh2EmZltrZIz9y3A/Ig4GDgKOFPSwcACYFlEHAQsS/MAx5M9FPsgYB5wQd1bbWZmZY2Z3CPisYj4XZp+GrgXmArMAi5Oi10MnJymZwGXROZ2YIqkfevdcDMzG50iovKFpS7gFuBQ4A8RMSWVC1gfEVMkLQUWpgdrI2kZcFZELC/Z1jyyM3s6OzsP7+vrqzqIoaEhOjo6ql6/HUyUGFYObhy1rnMSrN3UxMY0gGOAGVMn168xVZoo74dymhFDb2/viojoHqmu4sfsSeoAfgh8IiKeyvJ5JiJCUuX/JbJ1FgOLAbq7u6Onp2c8q2+lv7+fWtZvBxMlhnKPb5s/YwuLVk7sJzc6BhiY3VO/xlRporwfyml1DBXdLSNpZ7LEfllE/CgVrx3ubkk/16XyQWB6bvVpqczMzJqkkrtlBFwI3BsRX8lVXQvMSdNzgGty5R9Id80cBWyMiMfq2GYzMxtDJZ/djgZOA1ZKuiOVfRZYCCyRdAbwCPDeVHc9cAKwGngWOL2eDTYzs7GNmdzThVGNUn3sCMsHcGaN7TIzsxr4G6pmZgXk5G5mVkBO7mZmBeTkbmZWQE7uZmYF5ORuZlZATu5mZgXk5G5mVkBO7mZmBeTkbmZWQE7uZmYF5ORuZlZATu5mZgXk5G5mVkBO7mZmBeTkbmZWQE7uZmYFVMkzVL8naZ2ku3NlZ0salHRHep2Qq/uMpNWS7pf0tkY13MzMRlfJmftFwHEjlJ8XETPT63oASQcDpwCHpHW+KWnHejXWzMwqM2Zyj4hbgCcr3N4soC8iNkfEw2QPyT6ihvaZmVkVaulz/6iku1K3zZ6pbCrwaG6ZNanMzMyaSBEx9kJSF7A0Ig5N853A40AAXwD2jYgPSvo6cHtEXJqWuxC4ISKuGmGb84B5AJ2dnYf39fVVHcTQ0BAdHR1Vr98OJkoMKwc3jlrXOQnWbmpiYxrAMcCMqZPr15gqTZT3QznNiKG3t3dFRHSPVLdTNRuMiLXD05K+AyxNs4PA9Nyi01LZSNtYDCwG6O7ujp6enmqaAkB/fz+1rN8OJkoMcxdcN2rd/BlbWLSyqj+ptuEYYGB2T/0aU6WJ8n4op9UxVNUtI2nf3Ow7geE7aa4FTpG0q6T9gYOA39TWRDMzG68x/71LugLoAfaWtAb4HNAjaSZZt8wA8CGAiFglaQlwD7AFODMinm9Iy83MbFRjJveIOHWE4gvLLH8ucG4tjTIzs9r4G6pmZgXk5G5mVkBO7mZmBeTkbmZWQE7uZmYF5ORuZlZATu5mZgXk5G5mVkATexCN7VRXmfFdzMzAZ+5mZoXk5G5mVkBO7mZmBeTkbmZWQE7uZmYF5ORuZlZATu5mZgXk5G5mVkBO7mZmBTRmcpf0PUnrJN2dK9tL0o2SHkg/90zlkvQ1Sasl3SXpDY1svJmZjayS4QcuAr4OXJIrWwAsi4iFkhak+bOA44GD0utI4IL008wmiFYObzGw8MSW7btoxjxzj4hbgCdLimcBF6fpi4GTc+WXROZ2YIqkfevUVjMzq5AiYuyFpC5gaUQcmuY3RMSUNC1gfURMkbQUWBgRt6a6ZcBZEbF8hG3OA+YBdHZ2Ht7X11d1EENDQ3R0dFS9fjsYTwwrBzc2uDXV6ZwEaze1uhW1cQytNWPqZGD7e09Xq7e3d0VEdI9UV/OokBERksb+D7HteouBxQDd3d3R09NTdRv6+/upZf12MJ4Y5rbpqJDzZ2xh0cqJPdCoY2itgdk9wPb3nm6Eau+WWTvc3ZJ+rkvlg8D03HLTUpmZmTVRtcn9WmBOmp4DXJMr/0C6a+YoYGNEPFZjG83MbJzG/Owm6QqgB9hb0hrgc8BCYImkM4BHgPemxa8HTgBWA88CpzegzWZmNoYxk3tEnDpK1bEjLBvAmbU2yszMauNvqJqZFZCTu5lZATm5m5kVkJO7mVkBObmbmRWQk7uZWQE5uZuZFZCTu5lZATm5m5kVkJO7mVkBObmbmRWQk7uZWQE5uZuZFZCTu5lZATm5m5kVkJO7mVkBObmbmRVQTY9IlzQAPA08D2yJiG5JewFXAl3AAPDeiFhfWzPNzGw86nHm3hsRMyOiO80vAJZFxEHAsjRvZmZN1IhumVnAxWn6YuDkBuzDzMzKUPZM6ypXlh4G1gMBfDsiFkvaEBFTUr2A9cPzJevOA+YBdHZ2Ht7X11d1O4aGhujo6Kh6/XYwnhhWDm5scGuq0zkJ1m5qdStq4xhaa8bUycD2956uVm9v74pcr8lWaupzB94UEYOSXg7cKOm+fGVEhKQR/3tExGJgMUB3d3f09PRU3Yj+/n5qWb8djCeGuQuua2xjqjR/xhYWraz1T6q1HENrDczuAba/93Qj1NQtExGD6ec64GrgCGCtpH0B0s91tTbSzMzGp+rkLml3SXsMTwNvBe4GrgXmpMXmANfU2kgzMxufWj67dQJXZ93q7ARcHhE/lfRbYImkM4BHgPfW3kwzMxuPqpN7RDwEHDZC+RPAsbU0yszMauNvqJqZFdDEvKTeJrrqeNfK/Blb2vYuGDObeHzmbmZWQE7uZmYF5G4ZM2sbw12dze6mHFh4YtP21Sw+czczKyAndzOzAnJyNzMrICd3M7MCcnI3MysgJ3czswJycjczKyAndzOzAprwX2LqWnCdx2UxMyvhM3czswKa8GfuZma1qucIr8Mq7VFo1NAHPnM3MysgJ3czswJqWHKXdJyk+yWtlrSgUfsxM7NtNSS5S9oR+AZwPHAwcKqkgxuxLzMz21ajztyPAFZHxEMR8RegD5jVoH2ZmVkJRUT9Nyq9GzguIv5zmj8NODIiPppbZh4wL82+Bri/hl3uDTxew/rtwDG0B8fQHhxDZV4VEfuMVNGyWyEjYjGwuB7bkrQ8Irrrsa1WcQztwTG0B8dQu0Z1ywwC03Pz01KZmZk1QaOS+2+BgyTtL2kX4BTg2gbty8zMSjSkWyYitkj6KPAzYEfgexGxqhH7SurSvdNijqE9OIb24Bhq1JALqmZm1lr+hqqZWQE5uZuZFdCESO6SdpT0e0lLR6jbT9LNqf4uSSek8i5JmyTdkV7fan7Lt2pnuRheJWlZan+/pGm5ujmSHkivOc1t9TbtrDaG53PHoWUX1iUNSFqZ2rF8hHpJ+loaMuMuSW/I1bXFcagxholyHF4r6TZJmyV9qqSuLYY1qTGGsuvWTUS0/Qv4JHA5sHSEusXA36fpg4GBNN0F3N3qtlcYww+AOWn6GOD7aXov4KH0c880vedEiiHND7X695/aMQDsXab+BOAGQMBRwK/b7ThUG8MEOw4vB/4jcC7wqVz5jsCDwAHALsCdwMETKYZK1q3Xq+3P3NMZ4InAd0dZJICXpunJwB+b0a7xqCCGg4Gb0vTNvDhUw9uAGyPiyYhYD9wIHNfIto6mhhgmklnAJZG5HZgiaV/a6DhUYLQYJoyIWBcRvwX+raRqwgxrUiaGpmn75A6cD/wj8MIo9WcD75e0Brge+Fiubv/UjfALSW9uaCvLO5/yMdwJvCtNvxPYQ9LLgKnAo7nl1qSyVjif6mIA2E3Sckm3Szq5oa0sL4CfS1qRhr8oNdrvu52OQ7UxwMQ5DqOZSMehUetWrK2fxCTp7cC6iFghqWeUxU4FLoqIRZLeCHxf0qHAY8B+EfGEpMOBH0s6JCKeakrjkwpj+BTwdUlzgVvIvs37fFMaWIE6xPCqiBiUdABwk6SVEfFgg5s9kjeldrwcuFHSfRFxSwvaUYtaYvBxqJ9aYmhK/O1+5n408A5JA2QfwY6RdGnJMmcASwAi4jZgN7L+rM0R8UQqX0HWV/fqZjU8Z8wYIuKPEfGuiHg98N9S2QbaZxiHWmIgIgbTz4eAfuD1TWv51m0cbsc64Gqyj/l5o/2+2+U41BLDRDoOo5lIx6Eh645LMy9C1PICehj5Qt4NwNw0/TqyPncB+wA7pvIDyP4I9mrTGPYGdkjT5wLnpOm9gIfJLuLtmaYnWgx7ArvmlnmAFlwEA3YH9shN/4ps5NL8Miey9cXI37TTcagxhglzHHLLns3WF1R3IruYvT8vXlA9ZILFUPG6tb7aultmNJLOAZZHxLXAfOA7kv6BrC9rbkSEpL8BzpH0b2T9xB+OiCdb1+qtlcTQA3xRUpB1aZwJEBFPSvoC2Vg9kCXMCRUD2T/cb0t6geyT4sKIuKcFze0ErpYEWZK4PCJ+KunDABHxLbJrNicAq4FngdNTXbsch6pjYAIdB0mvAJaT3SjxgqRPkP0jekrNHdak7jGQ/WPdZt1GNNLDD5iZFVC797mbmVkVnNzNzArIyd3MrICc3M3MCsjJ3cysgJzczcwKyMndzKyA/h1l2Kqjh3axhAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "#Plotting the histograms for the 3 variables\n",
    "df.normal.hist();\n",
    "plt.title('Random Normal Histogram \\n (\\u03BC = 5, \\u03C3 = 0.05)');"
   ]
  },
  {
   "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": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df.uniform.hist();\n",
    "plt.title('Random Uniform Distribution Histogram \\n (a = 4.0, b = 5.5)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "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": [
    "df.binomial.hist()\n",
    "plt.title('Random Binomial Distribution Histogram \\n (n = 15, p = 0.05)');"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "#Storing the mean, median and desvest of the population\n",
    "parameters = {\n",
    "    \"uniform_dist\": {\n",
    "        \"mean\": df.uniform.mean(),\n",
    "        \"median\": df.uniform.median(),\n",
    "        \"std\": df.uniform.std()\n",
    "    },\n",
    "    \"normal_dist\": {\n",
    "        \"mean\": df.normal.mean(),\n",
    "        \"median\": df.normal.median(),\n",
    "        \"std\": df.normal.std()\n",
    "    },\n",
    "    \"binomial\": {\n",
    "        \"mean\": df.binomial.mean(),\n",
    "        \"median\": df.binomial.median(),\n",
    "        \"std\": df.binomial.std()\n",
    "    }\n",
    "}"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "{\n",
      "    \"uniform_dist\": {\n",
      "        \"mean\": 4.747806528172976,\n",
      "        \"median\": 4.759842615679644,\n",
      "        \"std\": 0.43976063753401085\n",
      "    },\n",
      "    \"normal_dist\": {\n",
      "        \"mean\": 5.001599754267347,\n",
      "        \"median\": 5.000861698922361,\n",
      "        \"std\": 0.04901432417153434\n",
      "    },\n",
      "    \"binomial\": {\n",
      "        \"mean\": 0.715625,\n",
      "        \"median\": 1.0,\n",
      "        \"std\": 0.822452811574647\n",
      "    }\n",
      "}\n"
     ]
    }
   ],
   "source": [
    "print(json.dumps(parameters, indent=4))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Building a function to generate m samples of the (mean, median, std...) of n-sized samples"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def get_sample_parameter_from_variable(m, n, df, parameter, \n",
    "                                       variable, random_state=42):\n",
    "    \"\"\"\n",
    "    Function that takes m random samples of n-size of the specified \n",
    "    dataframe column and applies the selected parameter \n",
    "    (mean, median, std) to each n-size sample. Returns an \n",
    "    m-size array with the sample parameters.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    m: int\n",
    "        Number of samples to take.\n",
    "    m: int\n",
    "        Sample size\n",
    "    df: pandas dataframe\n",
    "        Dataframe where each column is a dataset\n",
    "    parameter: str\n",
    "        Can be one of following: 'mean', 'median', 'std'\n",
    "    variable: str\n",
    "        Pandas dataframe column \n",
    "        (in our example can be one of following: 'normal', \n",
    "        'uniform', 'binomial')\n",
    "    random_state: int (optional):\n",
    "        Random seed number to initialize random number generator\n",
    "    \"\"\"\n",
    "    result = []\n",
    "    for x in range(m):\n",
    "        df_sample = df[variable].sample(n=n, \n",
    "                                        random_state = random_state)\n",
    "        if parameter == 'mean':\n",
    "            result.append(df_sample.mean())\n",
    "        elif parameter == 'median':\n",
    "            result.append(df_sample.median())\n",
    "        elif parameter == 'std':\n",
    "            result.append(df_sample.std())\n",
    "        random_state+=1\n",
    "    return list(result)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Example os usage: Let's say we want to get a list of the mean of 20 random samples (each one with size 35), from the binomial distribution variable."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0.8571428571428571,\n",
      " 0.4857142857142857,\n",
      " 0.6571428571428571,\n",
      " 0.6857142857142857,\n",
      " 0.7714285714285715,\n",
      " 0.7714285714285715,\n",
      " 0.7142857142857143,\n",
      " 0.5714285714285714,\n",
      " 0.7142857142857143,\n",
      " 0.7428571428571429,\n",
      " 0.5714285714285714,\n",
      " 0.8571428571428571,\n",
      " 0.9714285714285714,\n",
      " 0.7142857142857143,\n",
      " 0.8571428571428571,\n",
      " 0.6857142857142857,\n",
      " 0.8,\n",
      " 0.8,\n",
      " 0.7714285714285715,\n",
      " 0.8571428571428571]\n"
     ]
    }
   ],
   "source": [
    "sample_mean_from_binomial = get_sample_parameter_from_variable(20, \n",
    "                                                               35, \n",
    "                                                               df, \n",
    "                                                               'mean',\n",
    "                                                               'binomial')\n",
    "pprint.pprint(sample_mean_from_binomial)"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.8"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}