{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-pQMN8BHZ51n"
      },
      "source": [
        "# Teorema do Limite Central\n",
        "\n",
        "### SME0221 Inferência Estatística\n",
        "\n",
        "por **Cibele Russo**\n",
        "\n",
        "**ICMC/USP - São Carlos SP**\n",
        "\n"
      ],
      "id": "-pQMN8BHZ51n"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "LKqf-tVbZ51r"
      },
      "source": [
        "Fonte: https://blog.quantinsti.com/central-limit-theorem/"
      ],
      "id": "LKqf-tVbZ51r"
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lPY4fXlqZ51r"
      },
      "source": [
        "### Exemplo exponencial"
      ],
      "id": "lPY4fXlqZ51r"
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "0kigKWN4Z51s",
        "outputId": "f13c11be-4e24-46e7-c990-c9a97cb56fd2"
      },
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Population mean: 4.0\n",
            "Population standard deviation: 4.0\n"
          ]
        }
      ],
      "source": [
        "# Importing necessary libraries\n",
        "import warnings\n",
        "warnings.filterwarnings('ignore')\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "\n",
        "\n",
        "# rate parameter for the exponentially distributed population\n",
        "rate = 0.25\n",
        "\n",
        "#Population mean\n",
        "mu = 1/rate\n",
        "\n",
        "# Population standard deviation\n",
        "sd = np.sqrt(1/(rate**2))\n",
        "\n",
        "print('Population mean:', mu)\n",
        "print('Population standard deviation:', sd)"
      ],
      "id": "0kigKWN4Z51s"
    },
    {
      "cell_type": "code",
      "source": [
        "# drawing 50 random samples of size 2 from the exponentially distributed population\n",
        "sample_size = 2\n",
        "df2 = pd.DataFrame(index= ['x1', 'x2'] )\n",
        "\n",
        "for i in range(1, 51):\n",
        "    exponential_sample = np.random.exponential((1/rate), sample_size)\n",
        "    col = f'sample {i}'\n",
        "    df2[col] = exponential_sample\n",
        "\n",
        "# Taking a peek at the samples\n",
        "df2"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 223
        },
        "id": "MUsykku1a5Q8",
        "outputId": "3e08af78-845c-424e-83fd-1939aaaffb48"
      },
      "id": "MUsykku1a5Q8",
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "    sample 1  sample 2   sample 3   sample 4  sample 5  sample 6  sample 7  \\\n",
              "x1  1.941383  1.251136  14.400024  22.001170  1.072971  3.099897  2.131636   \n",
              "x2  4.661698  2.782234   1.737298   2.655372  6.947582  2.591737  7.541948   \n",
              "\n",
              "    sample 8  sample 9  sample 10  ...  sample 41  sample 42  sample 43  \\\n",
              "x1  0.898213  3.237277  13.164167  ...   2.299618   0.143017   0.720995   \n",
              "x2  0.457868  3.066978   3.985967  ...   6.665297   8.704233   0.696258   \n",
              "\n",
              "    sample 44  sample 45  sample 46  sample 47  sample 48  sample 49  \\\n",
              "x1  12.644751   0.102006   1.010089   9.012980   1.265512   0.859156   \n",
              "x2  10.097712   9.586246   4.592424   1.069703   0.021359   3.827212   \n",
              "\n",
              "    sample 50  \n",
              "x1   0.057872  \n",
              "x2   3.586337  \n",
              "\n",
              "[2 rows x 50 columns]"
            ],
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              "<style scoped>\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>sample 1</th>\n",
              "      <th>sample 2</th>\n",
              "      <th>sample 3</th>\n",
              "      <th>sample 4</th>\n",
              "      <th>sample 5</th>\n",
              "      <th>sample 6</th>\n",
              "      <th>sample 7</th>\n",
              "      <th>sample 8</th>\n",
              "      <th>sample 9</th>\n",
              "      <th>sample 10</th>\n",
              "      <th>...</th>\n",
              "      <th>sample 41</th>\n",
              "      <th>sample 42</th>\n",
              "      <th>sample 43</th>\n",
              "      <th>sample 44</th>\n",
              "      <th>sample 45</th>\n",
              "      <th>sample 46</th>\n",
              "      <th>sample 47</th>\n",
              "      <th>sample 48</th>\n",
              "      <th>sample 49</th>\n",
              "      <th>sample 50</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>x1</th>\n",
              "      <td>1.941383</td>\n",
              "      <td>1.251136</td>\n",
              "      <td>14.400024</td>\n",
              "      <td>22.001170</td>\n",
              "      <td>1.072971</td>\n",
              "      <td>3.099897</td>\n",
              "      <td>2.131636</td>\n",
              "      <td>0.898213</td>\n",
              "      <td>3.237277</td>\n",
              "      <td>13.164167</td>\n",
              "      <td>...</td>\n",
              "      <td>2.299618</td>\n",
              "      <td>0.143017</td>\n",
              "      <td>0.720995</td>\n",
              "      <td>12.644751</td>\n",
              "      <td>0.102006</td>\n",
              "      <td>1.010089</td>\n",
              "      <td>9.012980</td>\n",
              "      <td>1.265512</td>\n",
              "      <td>0.859156</td>\n",
              "      <td>0.057872</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>x2</th>\n",
              "      <td>4.661698</td>\n",
              "      <td>2.782234</td>\n",
              "      <td>1.737298</td>\n",
              "      <td>2.655372</td>\n",
              "      <td>6.947582</td>\n",
              "      <td>2.591737</td>\n",
              "      <td>7.541948</td>\n",
              "      <td>0.457868</td>\n",
              "      <td>3.066978</td>\n",
              "      <td>3.985967</td>\n",
              "      <td>...</td>\n",
              "      <td>6.665297</td>\n",
              "      <td>8.704233</td>\n",
              "      <td>0.696258</td>\n",
              "      <td>10.097712</td>\n",
              "      <td>9.586246</td>\n",
              "      <td>4.592424</td>\n",
              "      <td>1.069703</td>\n",
              "      <td>0.021359</td>\n",
              "      <td>3.827212</td>\n",
              "      <td>3.586337</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "<p>2 rows × 50 columns</p>\n",
              "</div>\n",
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              "    .colab-df-convert {\n",
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              "      border-radius: 50%;\n",
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              "    .colab-df-convert:hover {\n",
              "      background-color: #E2EBFA;\n",
              "      box-shadow: 0px 1px 2px rgba(60, 64, 67, 0.3), 0px 1px 3px 1px rgba(60, 64, 67, 0.15);\n",
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              "\n",
              "    [theme=dark] .colab-df-convert {\n",
              "      background-color: #3B4455;\n",
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              "\n",
              "    [theme=dark] .colab-df-convert:hover {\n",
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              "                                                     [key], {});\n",
              "          if (!dataTable) return;\n",
              "\n",
              "          const docLinkHtml = 'Like what you see? Visit the ' +\n",
              "            '<a target=\"_blank\" href=https://colab.research.google.com/notebooks/data_table.ipynb>data table notebook</a>'\n",
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          "metadata": {},
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      ]
    },
    {
      "cell_type": "code",
      "source": [
        "# Calculating sample means and plotting their distribution\n",
        "df2_sample_means = df2.mean()\n",
        "sns.distplot(df2_sample_means);"
      ],
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        "colab": {
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      },
      "id": "2pbh3DaYa_Wb",
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "hk9wlghjZ51v"
      },
      "outputs": [],
      "source": [
        "np.random.binomial"
      ],
      "id": "hk9wlghjZ51v"
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 265
        },
        "id": "ILZj03f7Z51w",
        "outputId": "8cf58cec-9861-450d-a916-63ef942c546e"
      },
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ],
            "image/png": 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Y5umLqwExPi2OqAiXDtOEMS14FTCby5vJTIwiOyna7ihhIcLtYlJmArtq2vHr4mNhSQteBURDRy8Vzd3MHZOC6Nz3gCnITqC9t5/KEVo+WIUWLXgVEJvLWxBg9phku6OElSmZibr4WBgbVsGLyEsicomI6D8I6qT5jWFLRTMTMuJJitGFxQIpJtJNflqcPtUapoZb2A8A1wN7ReQ/RGSKhZmUw5Q1dtHc5WWu3r3boiA7kfr2Xho6eu2OogJsWAVvjHnXGHMDMA84BLwrIp+IyC0iordk6rg2lzcT6XYxfXSS3VHC0jRdfCxsDXvIRURGATcDXwM2A79loPDfsSSZcgSvz8/Wqlamj04kMkJH+OyQEhtJdlK0DtOEoeGOwb8MfATEAv9gjLnUGPOcMeY7QLyVAVVo21nTRm+/n7k6991W07ITKW/sokMXHwsrw72lesQYU2CMuc8YUwMgIlEAxphCy9KpkLe5vIXE6Ahd991mny4+pnfxYWW4Bf/vx/jY2pEMopyno7efvXXtzBmj677bLTspmuQYj47Dh5mI431SRLKAHCBGROYCR35KExkYrlFqSCUVLfgNzM3T2TN2k8HFx4rLmujr9+vrIWHiuAUPXMzAC6u5wK8/8/F24EcWZVIOsbmimdHJ0WQm6tIEwaAgO5F1BxrZV9dBwehEu+OoADhuwRtjngCeEJGrjDEvBiiTcoDath6qW3q4ZGa23VHUoHFpcUR7BhYf04IPDycaornRGPM0kC8idx39eWPMr4/xZUqxubwFl+jSBMHE7RImZyaw63AbfmP0dZEwcKKBuCNTH+KBhGO8KfU5R5YmmJSRQHzUiUYBVSAVZCfS2eejvLHL7igqAE40RPPQ4H9/Gpg4ygkO1HfS1tPP8pl69x5sJmcm4BZhZ00b+Wk6ddXphvug0y9EJFFEPCLynojUi8iNVodToWlzeTPRHtenj8ir4BHtcTM+fWDxMaNrxDvecOdKXWSMaQNWMLAWzUTg+1aFUqGrr9/P9uo2ZuYk4dFt+YLStOxEGjv7qG/Xxcecbrg/gUeGci4B/myMabUojwpx26tb6fP5mTNGlyYIVkd+s9K1aZxvuAW/SkR2AfOB90QkHeixLpYKVZvLW0iJ9TB2lD4HF6ySYjyMSYlhW7XepzndcJcLvhtYDBQaY7xAJ3CZlcFU6Gnp6mN/fQdz83RpgmA3IyeJ6pYemjr77I6iLHQyg6RTgWtF5CvA1cBFxztYRKJFZIOIlIjIdhHRmTgOt6WiBQPM05Ujg96Rtfm3VeldvJMNa5KyiDwFTAC2AL7BDxvgyeN8WS9wnjGmY3BTkDUi8qYxZt3pBFbByRjDpvJm8kfFkRoXaXccdQKpcZHkJA8M05w9Od3uOMoiw30KpRAoMCcxr2rw2I7BP3oG33RelkNVNHXR0NHHF7QsQsaMnCTe2n6Y5q4+UmL1H2UnGu4QzTYg62S/uYi4RWQLUAe8Y4xZf4xjbheRIhEpqq+vP9lTqCCxqbwFj1uYodvyhYwZg+vRbNdhGscabsGnATtE5C0RefXI24m+yBjjM8bMYWA1ygUiMuMYxzxsjCk0xhSmp+vdXyjy+vyUVrUwfXQSUR633XHUMI2KjyI7KZpt1Tpd0qmGO0Rz7+mcxBjTIiKrgWUM/DagHGRnTRs9Xr++uBqCZuYk8faOWlq7vSTFeOyOo0bYcKdJfsjAE6yewfc3ApuO9zUiki4iyYPvxwAXArtOK60KSpvKm0mK8ei2fCFohs6mcbThrkXzdeAF4KHBD+UAr5zgy7KB1SJSysA/CO8YY1adalAVnNq6veyt7WBuXrLOfQ9BaQlRZCVGU1rZYncUZYHhDtHcASwA1gMYY/aKSMbxvsAYUwrMPb14Kth9OvddlyYIWbPHJPPW9sM0dfbpFFeHGe6LrL3GmE8feRORCHTKY9g7Mvc9LzWWtIQou+OoUzQrd2CYRu/inWe4Bf+hiPyIgc23LwT+DLxmXSwVCiqbu6lr79UXV0NcSmwkeamxlGjBO85wC/5uoB7YCnwDeAP4iVWhVGjYcKiJSLfr0ztAFbpm5yZR29bL4VZdQ9BJhjuLxs/Ai6rfMsZcbYx55GSealXO0+P1UVrZwqzcJKJ17nvIm5GThEvQu3iHOW7By4B7RaQB2A3sHtzN6f8EJp4KVlsqWvD6DAvGpdodRY2AhGgPE9LjKa1s0Z2eHOREd/D/DCwBzjDGpBpjUoGFwBIR+WfL06mgZIxh46EmRidFk5McY3ccNUJm5SbT3OWlornb7ihqhJyo4G8CrjPGHDzyAWPMAeBG4CtWBlPBq7K5m5rWHs4Yl4ro3HfHmD46kQiXsKVCh2mc4kQF7zHGNBz9QWNMPQOrQ6owdOTF1dm5yXZHUSMo2uNmanYipZUt9Pv9dsdRI+BEBX+87V50K5gwpC+uOtv8vGS6+nzsPtxudxQ1Ak70JOtsETnWUnMCRFuQRwW54rJmfXHVwSZmJJAQFcGmsuZPd31Soeu4BW+M0Vs09Smf37D2QCNjU2PJTdFNtZ3I7RLm5CXz8b4G2nu8dsdRp+lk9mRVYe69nbU0dfaxeGKa3VGUheblpeA3UFKpK0yGOi14NWyPfXyQpBgPBdmJdkdRFspMjCY3JYZNZc06Jz7EacGrYdlR3ca6A02cOX4UbpdOjXS6eXkpHG7rYbvu9hTStODVsDz+8UFiPG4K83VhsXAwKzcJt0t4objS7ijqNGjBqxNq6OjlLyXVXDU/h9jI4W4hoEJZbGQEBdmJvLSpkh6vz+446hRpwasTemzNQbw+PzcvHmd3FBVAC8el0tbTz6rSGrujqFOkBa+Oq6WrjyfXlrF8ZjYTM+LtjqMCaFxaHOPT43hmfZndUdQp0oJXx/X4x4fo6O3n2+dOtDuKCjAR4YaFY9lc3sL2ap0yGYq04NWQ2nu8PP7xQS4syGSaTo0MS1fNyyEqwsXK9eV2R1GnQAteDenJtWW09fTz3fMm2R1F2SQ5NpIVs0bzyuYqOnr77Y6jTpIWvDqmrr5+/rDmIOdMSWembskX1m5YlEdnn4+/bKmyO4o6SVrw6pgeW3OQps4+vnOejr2Hu7ljkpmWnchTa8v0ydYQowWvPqe+vZcHP9jPRQWZzB+rq0aGOxHhlsX57Drczif7G+2Oo06CFrz6nPvf3UNvv5+7vzjV7igqSFw6ZzRp8ZE8+tEBu6Ook6AFr/7O3tp2/rSxghsW5jE+Xee9qwHRHjc3LhrL6t317KvrsDuOGibLCl5ExojIahHZISLbReROq86lRs59b+4i1uPmzgsm2x1FBZkbF40lMsLF4x8fPPHBKihYeQffD3zPGFMALALuEJECC8+nTtNHe+t5f1cdd5w3kdS4SLvjqCCTFh/F5XNG8+KmSpo7dcfOUGBZwRtjaowxmwbfbwd2AjlWnU+dnu4+Hz95ZRv5o2K5eXG+3XFUkLpt6Xh6vH5WbtAHn0JBQMbgRSQfmAusP8bnbheRIhEpqq+vD0QcdQz3v7eHssYufn7lTN1MWw1pSlYCZ01K4/GPD+kqkyHA8oIXkXjgReCfjDGf2z3AGPOwMabQGFOYnp5udRx1DNuqWnn0o4NcWziGxRN0Oz51fN86ZyINHb08X1RhdxR1ApYWvIh4GCj3Z4wxL1l5LnVq+n1+7n6plJTYSH60fJrdcVQIWDQ+lfljU3jowwP09fvtjqOOw8pZNAL8AdhpjPm1VedRp+d/P9zPtqo2fnrpdJJiPXbHUSFARPj2eROpaunmlc26fEEws/IOfglwE3CeiGwZfFtu4fnUSSoua+I37+5lxaxsls/MsjuOCiHnTE5nRk4iD3ywD59fly8IVlbOolljjBFjzCxjzJzBtzesOp86Oa1dXr777BZykmP4+ZUzGfiFS6nhERG+fe5EDjV2saq02u44agi6wWYIOt21uY0xrNxQTk1rN9/8wgRWleiWbOrYjvd3zW8MGQlR/Oz1nbT39OMa4ZuE6xfmjej3C0e6VEEYWnugke3VbVw8PYvclFi746gQ5RLhvKkZ1LX3UlLRYnccdQxa8GFmX10Hb2ytYVpWAksm6pRIdXpm5CSRnRTNuztr6ffrjJpgowUfRho6elm5oYz0hCi+VDhmxH+lVuHHJcJFBVk0d3kpOtRsdxx1FC34MNHj9fHU2jJcIty0KJ8ofVpVjZDJmfGMHRXL6t11Oi8+yGjBh4F+n5+n15fR2NnL9QvzdCExNaJEhIsLsmjv6WfdAd0QJJhowTuc3xieL67kQH0nV83LZXyarvGuRl5+WhxTMhP4YE8dXbo5d9DQgncwYwyvlVSzraqVL87IYm5eit2RlIMtm5FFr9fPu7vq7I6iBmnBO9j7u+tYf7CJsyalcdYkXchNWSszMZoF41LZcLCR2rYeu+MotOAda/3BRt7bWce8vGSWTddlCFRgXDAtk8gIF29u04fngoEWvANtq2rl1S3VTMlM4Iq5uboMgQqYuKgIzpuayZ7aDnYfbrc7TtjTgneYA/UdPFdUwZjUWK5bkIfbpeWuAmvR+FRGxUXy+tYaffjJZlrwDlLd0s1T68oYFRfJV84c2CBZqUCLcLlYMSubho5e1uxtsDtOWNMGcIimzj7++Mkhoj1ublkyjthIXUdO2WdKViLTRyeyencdTbpBt2204B2gs7efP35yEJ/fcMvifJJidOMOZb8Vs0YjIrxWUo0xuma8HbTgQ5zX5+epdWW0dHn5ypljyUiMtjuSUgAkxXi4YGoGu2vb2VHzue2YVQBowYcwvzE8t7GCiqYuvlQ4hrGj4uyOpNTfOXNCGtlJ0bxWUk2P12d3nLCjBR+ijDGsKq1hR00bl8zKZkZOkt2RlPoct0u4fE4O7T39vLntsN1xwo4WfIhas6+BdQcaWToxjcUTdF13FbzGpMaydGIaGw81sa+uw+44YUULPgTtqmnjr9sOMyMniWUz9ClVFfwuKMhkVFwkL2+upLdfh2oCRQs+xOytbee5ogqyk6O5el6ubtqhQoLH7eKqebm0dHl5a3ut3XHChhZ8CGnp6uPrTxbhcbu4caE+yKRCS35aHIsmjGLdgUYdqgkQbYgQ0e/z8+2Vm6lu6eGGhXkkx+qmHSr0XFyQRVp8FC8UV9DVp+vGW00LPkT8/I1drNnXwL9fPkOnQ6qQFRnh4trCMXT09vPKFn0Aympa8CHgpU2VPPbxQW5dMo4vnTHG7jhKnZaclBgunJbJtqpWtlS02B3H0SwreBF5TETqRGSbVecIB7sOt/Gjl7eyaHwqP1o+1e44So2Isyankz8qlldLqmns6LU7jmNZeQf/R2CZhd/f8Tp6+/nWM5tIiPbwu+vmEuHWX7iUM7hEuKZwDC4Rnt1QjtenywpbwbLGMMb8DWiy6vs7nTGGf32xlEMNnfz3dXPJSNA1ZpSzpMRGcs38XKpbe3i9VHeAsoLtt4QicruIFIlIUX19vd1xgsaTa8t4vbSGf7l4CovGj7I7jlKWmJqdyNmT0tlwqIktFc12x3Ec2wveGPOwMabQGFOYnq4bQwNsqWjh31/fwflTM/jm2RPsjqOUpS4syCR/VCyvbK6mTjfrHlG2F7z6e82dfdzxzCYyEqL51Zdm49It95TDuV3Cl8/Iw+MWVm4op69fx+NHihZ8EPH7DXc9v4X69l4euGGePsykwkZijIdrz8ijvr2XlzdX6vz4EWLlNMlngbXAFBGpFJHbrDqXUzz44X5W767nnhXTmD0m2e44SgXUxIx4LijIpKSylb/t0dfjRoJlG3caY66z6ns70Sf7G/jV27v5h9mjuXHRWLvjKGWLcyanU9vWw9s7anl7+2Eumq6rpZ4OHaIJArVtPXz32S3kp8Vx35UzEV0hUoUpEeGqebnkpMTwT89tYadu9XdatOBt5vX5+fbKTXT29vO/N84nPsqyX6qUCglHVktNiI7ga08U0aBPup4yLXib/eebu9h4qJn/uGomkzMT7I6jVFBIjPHwyFcKaezs5ZtPFesmIadIC95Gb2yt4dE1B/nqmWO5bE6O3XGUCiqzcpP55TWzKSpr5nvPl+D368yak6XjATbZX9/B9/9cwpwxyfz4kgK74ygVlFbMGk1Vczf3vbmL9IQo/tm1M+EAAAoSSURBVM+KAn2N6iRowdugq6+ff3y6mCiPmwdumKc7Myl1HLefPZ669l7+sOYgGQnR/OM5+nT3cGnBB5gxhh+8UMreug6eunUho5Nj7I6kVFATEX68fBr17b385193kRo38FCUOjEt+AD7n/f3saq0hn9dNpWlk9LsjqNUSHC5hF9eM5vWbi93v7SVyAgXV8zNtTtW0NOxgQD667bD/OqdPVwxN4dvfmG83XGUCimRES4eumk+Z44fxfeeL2FVabXdkYKeFnyA7Khu45+f28LsMcn6MJNSpyja4+bRrxYyf2wKd/5pC29u1XXkj0cLPgCqWrq59Y8bSYrx8MhN84n2uO2OpFTIio2M4LGbz2DOmGTuWLmJF4sr7Y4UtLTgLdbS1cdXH9tAZ18/j99yBhmJujOTUqcrIdrDk7cu4MwJo/jen0t4al2Z3ZGCkha8hbr7fNz2RBHljV088pVCpmUn2h1JKceIi4rgD189gwumZXDPK9v47/f26jLDR9GCt0iP18e3nilmU3kz9395jm67p5QFoj1uHrxxPlfMzeFX7+zhBy+U6gben6HTJC3Q4/XxjaeK+XBPPT+/YibLZ2bbHUkpx/K4Xfz6S7MZkxrL797bS3VrNw/cMJ+kGI/d0Wynd/AjrMfr4+tPFvHhnnruu3Im1y/UBzKUspqIcNeFk/nlNbPZcLCJy/5njS41jBb8iGrt9nLL4xtZs6+BX1w1i+sWaLkrFUhXz89l5dcX0dXn44oHPualTeE9w0YLfoRUNHVx1YOfUFTWxK+/NJsvnTHG7khKhaUz8lNZ9d2lzBmTzF3Pl/CDF0po7/HaHcsWWvAjoLismct//zH17b08eetCfYRaKZtlJETz9G0LuePcCbxQXMmy+z9i7f5Gu2MFnBb8afD7DQ99uJ8vP7yW+OgIXvrWYs6coLNllAoGEW4X3794Kn/+5pl43MJ1j6zjnle20dLVZ3e0gNGCP0W1bT3c9Nh67ntzF+dPzeQvdyxhQnq83bGUUkeZPzaVN+48i5sX5/PM+jLO/eUHPLuhHF8YbCCiBX+S+n1+nvjkEBf++kOKy5q578qZPHjjPJJjI+2OppQaQmxkBPdeOp1V3zmLSRkJ/PClrVzyu4/467bDjt4pSufBn4S1+xv56Wvb2XW4ncUTRvFvl81gYobetSsVKgpGJ/LcNxbxWmkNv3lnD998upiC7ES+fd5ELirIJMLtrHteLfgTMMawencdD36wn42HmslJjuHBG+axbEaWrgipVAgSES6dPZrlM7L4y5Zq/vv9vXzrmU1kJ0Vz/YI8rl0whowEZ6wZpQU/hMOtPfxlSxUvFFeyt66DnOQY7v2HAq49I4+YSF0NUqlQF+F2cdX8XC6fm8N7O2t5al0Zv3pnD795dw9nThjFilmjuXh6FqlxoTv8KsG0OE9hYaEpKiqy5dzGGPbUdvC3PfWs3l3H2gONGANzxiRz06KxXDpnNJ4g+fVt5fpyuyMoZTk7ngI/UN/BK5ureK20hoMNnYjArJwklk5KY8mENGaNSSY+Krjui0Wk2BhTeMzPWVnwIrIM+C3gBh41xvzH8Y4PVMF7fX4qm7s5UN/Btqo2tla1UlLZQn17LwATM+JZPiOLy+fmMD4IZ8ZowatwYOcyH8YYtle38d7OOj7aW8/mihZ8foMITMqIZ0ZOEhPS45mQHsf49HjGjoolKsKe3+yPV/CW/VMkIm7g98CFQCWwUUReNcbsGOlzVTZ30dXno7O3/+/+29Xno7mrj/r2Xuo7eqlv76WurYfK5m76B185F4EJ6fEsnZjGmeNHsXRSmm6ErVSYExFm5CQxIyeJOy+YRFuPl+KyZkoqWiipaGHN3gZe2lT16fEugfSEqIG3+CgyEqJJS4gkIdpDXFQECVERxEVFEBflJj4qgqgIN5ERLiIjXHjcQlSE25LF0az8XWMBsM8YcwBARP4EXAaMeMGf/6sP6e0feonQhKgI0hOiSEuIYnpOEstnZpOfFsf4tDimZicG3a9cSqngkhjt4dwpGZw7JePTj3X09nOwvpMDDR3sr+/kcGv3pzeT26vbaOzsG/Zc+7T4SIp+cuGI57ay2XKAis/8uRJYePRBInI7cPvgHztEZPcI50gDGkb4ezqFXpuh6bUZWkCuzQ1Wn8Aap3RtygC555TPOXaoT9h+62qMeRh42KrvLyJFQ41PhTu9NkPTazM0vTZDC7ZrY+W0kCrgs0sq5g5+TCmlVABYWfAbgUkiMk5EIoEvA69aeD6llFKfYdkQjTGmX0S+DbzFwDTJx4wx260633FYNvzjAHpthqbXZmh6bYYWVNcmqB50UkopNXKC49FMpZRSI04LXimlHMoRBS8i0SKyQURKRGS7iPz0GMfkichqEdksIqUistyOrIE2zGszVkTeG7wuH4hIWO05KCLuwb8Xq47xuSgReU5E9onIehHJD3xC+5zg2pwtIptEpF9ErrYjn51OcG3uEpEdgz9T74nIkHPVreSIggd6gfOMMbOBOcAyEVl01DE/AZ43xsxlYEbPAwHOaJfhXJtfAk8aY2YB/wbcF+CMdrsT2DnE524Dmo0xE4HfAP8ZsFTB4XjXphy4GVgZsDTB5XjXZjNQOPgz9QLwi4Cl+gxHFLwZ0DH4R8/g29GvHhsgcfD9JKA6QPFsNcxrUwC8P/j+agaWlAgLg7+tXAI8OsQhlwFPDL7/AnC+hMlGACe6NsaYQ8aYUmDodUIcahjXZrUxpmvwj+sYeA4o4BxR8PDpr0tbgDrgHWPM+qMOuRe4UUQqgTeA7wQ4om2GcW1KgCsH378CSBCRcNk9/H7gBwxdUp8uuWGM6QdaAb026mSuzW3Am9bGOTbHFLwxxmeMmcPAv5QLRGTGUYdcB/zRGJMLLAeeEhHH/P8fzzCuzb8AXxCRzcAXGHji2BfgmAEnIiuAOmNMsd1Zgo1em6GdzLURkRuBQuC/LA92DI4rOGNMCwPDDMuO+tRtwPODx6wFohlYGChsDHVtjDHVxpgrB1+f+PFnjnW6JcClInII+BNwnog8fdQxny65ISIRDAzvNQYypE2Gc23C1bCujYhcwMDP06XGmN7ARhzgiIIXkXQRSR58P4aBNeh3HXVYOXD+4DHTGCj4+kDmtMNwro2IpH3mt5kfAo8FNqU9jDE/NMbkGmPyGXjh/X1jzI1HHfYq8NXB968ePMbxTwcO89qEpeFcGxGZCzzEQLnX2RATcEjBA9nAahEpZWANnHeMMatE5N9E5NLBY74HfF1ESoBngZvD4QeV4V2bc4DdIrIHyAR+Zk/U4HDUtfkDMEpE9gF3AXfbl8x+n702InLG4Gta1wAPiYgdS5EEjaP+3vwXEA/8WUS2iIgt63DpUgVKKeVQTrmDV0opdRQteKWUcigteKWUcigteKWUcigteKWUcigteKWUcigteKWUcqj/B1hLJtE0gYPZAAAAAElFTkSuQmCC\n"
          },
          "metadata": {
            "needs_background": "light"
          }
        }
      ],
      "source": [
        "# drawing 50 random samples of size 500\n",
        "sample_size=5000\n",
        "\n",
        "df500 = pd.DataFrame()\n",
        "\n",
        "for i in range(1, 51):\n",
        "    exponential_sample = np.random.exponential((1/rate), sample_size)\n",
        "    col = f'sample {i}'\n",
        "    df500[col] = exponential_sample\n",
        "\n",
        "\n",
        "df500_sample_means = pd.DataFrame(df500.mean(),columns=['Sample means'])\n",
        "sns.distplot(df500_sample_means);"
      ],
      "id": "ILZj03f7Z51w"
    },
    {
      "cell_type": "code",
      "source": [
        "df500_sample_means"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 1000
        },
        "id": "lR0A1xA3bdZc",
        "outputId": "bdf00567-00bc-4385-dda7-ed878c1f03aa"
      },
      "id": "lR0A1xA3bdZc",
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "           Sample means\n",
              "sample 1       3.958604\n",
              "sample 2       4.045756\n",
              "sample 3       4.116816\n",
              "sample 4       3.987188\n",
              "sample 5       3.996352\n",
              "sample 6       3.883661\n",
              "sample 7       4.014121\n",
              "sample 8       4.013331\n",
              "sample 9       4.050435\n",
              "sample 10      4.016005\n",
              "sample 11      3.966928\n",
              "sample 12      4.136723\n",
              "sample 13      3.983414\n",
              "sample 14      3.890308\n",
              "sample 15      4.091705\n",
              "sample 16      4.019620\n",
              "sample 17      3.874229\n",
              "sample 18      4.021794\n",
              "sample 19      4.005865\n",
              "sample 20      4.054779\n",
              "sample 21      4.049871\n",
              "sample 22      4.093898\n",
              "sample 23      3.944739\n",
              "sample 24      3.998640\n",
              "sample 25      3.947447\n",
              "sample 26      4.096262\n",
              "sample 27      3.933521\n",
              "sample 28      4.056726\n",
              "sample 29      3.946058\n",
              "sample 30      4.025021\n",
              "sample 31      4.031176\n",
              "sample 32      3.941051\n",
              "sample 33      3.967591\n",
              "sample 34      4.061080\n",
              "sample 35      4.004738\n",
              "sample 36      3.964225\n",
              "sample 37      4.008443\n",
              "sample 38      3.944334\n",
              "sample 39      4.054432\n",
              "sample 40      4.064087\n",
              "sample 41      3.992023\n",
              "sample 42      3.890063\n",
              "sample 43      4.061847\n",
              "sample 44      4.032388\n",
              "sample 45      4.045628\n",
              "sample 46      3.928111\n",
              "sample 47      3.959733\n",
              "sample 48      3.988483\n",
              "sample 49      4.025135\n",
              "sample 50      3.981385"
            ],
            "text/html": [
              "\n",
              "  <div id=\"df-4958e447-1e56-480b-992b-a09fc806225d\">\n",
              "    <div class=\"colab-df-container\">\n",
              "      <div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        vertical-align: middle;\n",
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              "  <thead>\n",
              "    <tr style=\"text-align: right;\">\n",
              "      <th></th>\n",
              "      <th>Sample means</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>sample 1</th>\n",
              "      <td>3.958604</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 2</th>\n",
              "      <td>4.045756</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 3</th>\n",
              "      <td>4.116816</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 4</th>\n",
              "      <td>3.987188</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 5</th>\n",
              "      <td>3.996352</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 6</th>\n",
              "      <td>3.883661</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 7</th>\n",
              "      <td>4.014121</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 8</th>\n",
              "      <td>4.013331</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 9</th>\n",
              "      <td>4.050435</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 10</th>\n",
              "      <td>4.016005</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 11</th>\n",
              "      <td>3.966928</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 12</th>\n",
              "      <td>4.136723</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 13</th>\n",
              "      <td>3.983414</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 14</th>\n",
              "      <td>3.890308</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 15</th>\n",
              "      <td>4.091705</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 16</th>\n",
              "      <td>4.019620</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 17</th>\n",
              "      <td>3.874229</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 18</th>\n",
              "      <td>4.021794</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 19</th>\n",
              "      <td>4.005865</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 20</th>\n",
              "      <td>4.054779</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 21</th>\n",
              "      <td>4.049871</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 22</th>\n",
              "      <td>4.093898</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 23</th>\n",
              "      <td>3.944739</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 24</th>\n",
              "      <td>3.998640</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 25</th>\n",
              "      <td>3.947447</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 26</th>\n",
              "      <td>4.096262</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 27</th>\n",
              "      <td>3.933521</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 28</th>\n",
              "      <td>4.056726</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 29</th>\n",
              "      <td>3.946058</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 30</th>\n",
              "      <td>4.025021</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 31</th>\n",
              "      <td>4.031176</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 32</th>\n",
              "      <td>3.941051</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 33</th>\n",
              "      <td>3.967591</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 34</th>\n",
              "      <td>4.061080</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 35</th>\n",
              "      <td>4.004738</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 36</th>\n",
              "      <td>3.964225</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 37</th>\n",
              "      <td>4.008443</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 38</th>\n",
              "      <td>3.944334</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 39</th>\n",
              "      <td>4.054432</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 40</th>\n",
              "      <td>4.064087</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 41</th>\n",
              "      <td>3.992023</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 42</th>\n",
              "      <td>3.890063</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 43</th>\n",
              "      <td>4.061847</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 44</th>\n",
              "      <td>4.032388</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 45</th>\n",
              "      <td>4.045628</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 46</th>\n",
              "      <td>3.928111</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 47</th>\n",
              "      <td>3.959733</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 48</th>\n",
              "      <td>3.988483</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 49</th>\n",
              "      <td>4.025135</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>sample 50</th>\n",
              "      <td>3.981385</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>\n",
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              "  "
            ]
          },
          "metadata": {},
          "execution_count": 8
        }
      ]
    }
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    "colab": {
      "name": "ExemploTLC.ipynb",
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