statistical_thinking_in_python.ipynb

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  "metadata": {
    "colab": {
      "name": "statistical-thinking-in-python.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/martin-fabbri/colab-notebooks/blob/master/statistical_thinking_in_python.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "lZ0aCrSWWPc-",
        "colab_type": "text"
      },
      "source": [
        "# Statistical thinking in Python"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M3IKTRWcPoIc",
        "colab_type": "text"
      },
      "source": [
        "## Exploratory Data Analysis"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5vGHijTaPlhO",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import matplotlib.pyplot as plt\n",
        "import seaborn as sns\n",
        "import numpy as np\n",
        "import pandas as pd\n",
        "\n",
        "from sklearn.datasets import load_iris\n",
        "from math import sqrt\n",
        "from scipy import stats\n",
        "sns.set()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Gf4Lp8JvOWGi",
        "colab_type": "code",
        "outputId": "f5f0ad30-a52e-4ab3-d73e-0dc07f48ecf3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 140
        }
      },
      "source": [
        "iris = load_iris()\n",
        "data = iris.data\n",
        "target = iris.target\n",
        "\n",
        "sentosa_samples = data[target == 0]\n",
        "versicolor_samples = data[target == 1]\n",
        "virginica_samples = data[target == 2]\n",
        "\n",
        "setosa_petal_length = sentosa_samples[:,0]\n",
        "versicolor_petal_length = versicolor_samples[:,0]\n",
        "virginica_petal_length = virginica_samples[:,0]\n",
        "\n",
        "setosa_petal_width = sentosa_samples[:,3]\n",
        "versicolor_petal_width = versicolor_samples[:,3]\n",
        "virginica_petal_width = virginica_samples[:,3]\n",
        "\n",
        "iris_df = pd.DataFrame(data=np.c_[iris['data'], iris['target']], \n",
        "                       columns=iris['feature_names'] + ['target'])\n",
        "iris_df.head(3)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/html": [
              "<div>\n",
              "<style scoped>\n",
              "    .dataframe tbody tr th:only-of-type {\n",
              "        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>sepal length (cm)</th>\n",
              "      <th>sepal width (cm)</th>\n",
              "      <th>petal length (cm)</th>\n",
              "      <th>petal width (cm)</th>\n",
              "      <th>target</th>\n",
              "    </tr>\n",
              "  </thead>\n",
              "  <tbody>\n",
              "    <tr>\n",
              "      <th>0</th>\n",
              "      <td>5.1</td>\n",
              "      <td>3.5</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>1</th>\n",
              "      <td>4.9</td>\n",
              "      <td>3.0</td>\n",
              "      <td>1.4</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "    <tr>\n",
              "      <th>2</th>\n",
              "      <td>4.7</td>\n",
              "      <td>3.2</td>\n",
              "      <td>1.3</td>\n",
              "      <td>0.2</td>\n",
              "      <td>0.0</td>\n",
              "    </tr>\n",
              "  </tbody>\n",
              "</table>\n",
              "</div>"
            ],
            "text/plain": [
              "   sepal length (cm)  sepal width (cm)  ...  petal width (cm)  target\n",
              "0                5.1               3.5  ...               0.2     0.0\n",
              "1                4.9               3.0  ...               0.2     0.0\n",
              "2                4.7               3.2  ...               0.2     0.0\n",
              "\n",
              "[3 rows x 5 columns]"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "0WYqBt6EWeye",
        "colab_type": "code",
        "outputId": "42ca4765-266e-4b64-baca-80ff4ce1c822",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "source": [
        "plt.xlabel('Petal length (cm)')\n",
        "plt.ylabel('Count')\n",
        "plt.hist(versicolor_petal_length);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EAM2SX4RCRkaGkpOTlZOTo+TkZM2fP9/qkgCgWbJ85rWysjLt27dPq1evliSNHDlSixYt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\nYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "falcouIWWevu",
        "colab_type": "code",
        "outputId": "85e465e5-6d0e-402b-9db9-6b9865b6583c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "n_data = len(versicolor_petal_length)\n",
        "n_bins = int(sqrt(n_data))\n",
        "\n",
        "print(f'Number on bins: {n_bins}')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Number on bins: 7\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WchZSW9GWetZ",
        "colab_type": "code",
        "outputId": "dcc2f800-9d32-4b82-e844-163b115281e2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "plt.hist(versicolor_petal_length, bins=n_bins);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Zs/Xss89GY9yIC2Z95syZo++//15dunSRJI0cOVKvvPJKxGeNhuvXr2vRokU6cOCA4uPj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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ayYiHV2uWeqs",
        "colab_type": "code",
        "outputId": "3ca5eefb-9d5b-4a55-8e98-a63ca76c9831",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "source": [
        "sns.swarmplot(x='target', y='petal length (cm)', data=iris_df);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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CfXym39TK7iPbcUQmHU/6AB0NGPK+hHnW10FvRBfire8OmvpljDnz0RydqC01\n2D9+xneIZm/HWfARrhMfEmsqaksVIbc8hdrVjC4ypdtEYZqm4sxf6R9n/gp0kcl+vxTchzahTrne\nOx+QOG+flq3zJX2ArbU7uCpjIVHmyH6MKrB6lPjvvfdeUlNT+dnPfobFIgNOxABwwmpZvtcnt4Ff\nZY7fvoYg0Pv/76Hojd7BXac6j6YC/s+gNE0FvQHFEOSX9DXVg9ZeD8FRcPIjNk3rdp6jG07RJs6F\neoq/3wB51NlrepT4Dx48yNKlS9FJP6MYIEy5l/vNuWPMvRx93HDc5bt9yV6fmospdxHugxvQuryr\nOCnBkbjLduNY/29Q9Bhz5mOe8VXvHD473gXVjS5xFEp4Atqx0k2TFVPOZd5ZPYvWH72igi46lY5/\n3+Od3iEmHcvC/0HrasH20TNonU0oljAMwyfhPrjhhLgXoYtIxFax1/cFYxg28bTPB8TZm5M6k6KW\nQ74vgLzYcURbhtZMqj2q6vnOd77D3XffTU5OTiBiOiWp6hFny12+G0/tIfQJWRhSvP92PU0VuEu2\nowuNwZAxDUVvQLW1HU2+irf75eizgWPMc76N/aTRvca8xeiCI7xr7mZORxcSjaaquEu2oTZXok8Y\nie3DP/p1LRlHX4qnsRS1vsTXpoQnYJ5xE566EvSJozAkj/HG2ViG+8hOdGGxGDKmoujkcVxvKm+v\nYnfDXmIt0UyKG49ep+/vkHrdOZVzPv30077/bm1t5b333mPBggXExMT47XfPPff0YqinJ4lfBMIp\nyznHzMO17+RyzulY5p7+gaun4Qhdbz3i16ZPHIWnofT4yl0AKITc8Xep2hG97pzKOWtqavxez5kz\nB7fb3a1diMHEkDbeP/HrDRizL8V1cAO4jo+6VUJj6Vr+GzS3A9OYuRhHzUJtq8ex5XXU5mr0aeNQ\nQqL9Hhwb0vK8XUnFm46fPi1Xkr4IOBnAJcRJXAc34Ny3yjtlQ95iDMlj8NQdxnF0EjbDsEk4dyzz\n68axXP4THJteQ22u8LUZR89Gs3egtjdgGDEZU96XwOXAsfVNPNVF6ONGEDT1BhTzqe/KhDgf5z1y\nd+rUqWzZsqVb+4wZM9i4ceP5R9gDkvjFhcJV+Bn2tX/3azNkXeT3kBZAF5lC8A1PBDI0IXzOe+Su\ny+U6ZZuqnqKsTYgBSFPduIs3o7bVYUifgD52mP92lx3XwQ3eaZkjErsdr4sZBmW7/Obz0UUk4Cr6\nHLWtHsOwiehj0gFwVxTgqS5EH5fhnfBNiAA7Y+K/+eabURQFp9PJLbfc4retpqaGCRMm9GlwQgSK\n/ZO/4D6yHQDnznexXPZDDDh8dsoAACAASURBVOnef9+aqtK1/NeoDaXenfUmDCNn4i7eCKoHw7BJ\nmLIvRRcciX3dS+DsQheZjOrowL7mb0fPuRzLoh+hNlX4RhQDmCZcKWvzioA7Y+K/4YYb0DSNPXv2\n8OUvf9nXrigK0dHRTJ8+vc8DFKKvqe0NvqQPgKbhLPjYl/g91QeOJ30AjxNFZyDktj+heVzojs7v\nYxwxBUPaeLSuVlA9dL5+/wnnVHEWfIzaWOZ3bWfBx5gmXyuzdIqAOmPiv/baawEYP348GRkZAQlI\niIBTdICC3+hYRYfa1Ypmaz26/SQ6PZrLjuZywIkTu3lcaM5OMJhPcRl993MpytFrCxE4Perj37lz\nJzt37uzWbjKZSEhIIC8vD5Pp1ItLC3Gh04VEYRh50fFRtzo9SnAknS//GDQPSkQSutgRqPWHvdtN\nFjRbm3cpRTT0iaOxLPoR7sNbsH/+L/C4UEKi0afm4inf7T1Gb8CYuwh9cxWOz//pu7Yp78puc/gI\n0dd6VNVz2223sXPnTmJiYkhISKCmpoaGhgZycnKorPTOUPjnP/+ZceP6bkUhqeoRfUnTVDxlu1Hb\natFFD8O28jd+8+gYsudgSBqNZmtHCY7A/vGzfsebpt6Ac+dyv8FZ+rQ8TKNno7Z7Hxgfm3bBU3cY\nT00hurgMDAkjA/MGxZBz3lU9mZmZLFiwgK997Wu+tv/85z8cPnyYpUuX8pe//IUnnniC11577Qxn\n8Xr22Wd55plnWL58OSNHyj96cWFQFJ2vwsZdc7Db5GlaRyPGjGkAuIo+73a82lx10ohc0DoaMAzr\nXgChjxuBPm5Eb4UuxFnrUeJfsWIFmzdv9mv76le/yvTp03n44Ye54447+Pvf/36ao4/bu3cv+fn5\nJCcnn1u0QvQC1+Gt3rtzjxtjzgJMY+bgaSzHsWkpamst+vQJKMFRaJ1NvmN0kcl0LnvcO4Br+GTv\nLJ2+RK94R+62VPnNw6OPz6RrxRLU9noMwycTNPXLaE4bjg0vHx/AddEt6IKHznTA4sLQo8QfHR3N\nqlWrmD9/vq9tzZo1REV5Z7RzOBwYDGc+ldPp5LHHHuP3v/+93y8HIQLJ01yF/dM/++7oHZ//EyU0\nBse6l3yJ3r33E4xj5nof3nY0oU/Pw7n1LfA4AXDteg/ThKtQmyvR3A6MR7uBdAvvwbl9GWpzFfrU\ncTj3fAz2Nu8xuz9AMVlQG8p8FUTukiY0RyfWxT/rh09CDGU9SvwPPfQQ99xzD1lZWSQmJlJdXc3B\ngwd9E7nt2rWL22677YznePrpp7nqqqtISUk5/6iFOEeeyn3dunHch7b43d0DeOqPEHztwwC4juzw\nJf1j1LY6LJfd7dems0ZgnvUN3/EnrqwF4KnYi+ekck5P1X40VZX5ekRA9Sjxz5w5k08++YS1a9dS\nV1fH7NmzmT17NpGRkb7tM2fOPO3xO3fupKCggHvvvfecAz3dQwohzoYtYxTV/jMrEJE1jsbS7WiO\n46vLWRPTMR5eg6etgbDUbOwnlXuGJKSgFH6I6rQRmjsHU0wKmttF++7VOBvKCUnLwWY0o53Q7x+c\nkoHDoMNRccDXZoxNIy4+vM/erxCnEpBJ2l544QX+9a9/+Uo+a2pqiI6O5te//vUZvzBOJFU9orc4\ntr2Fc9cHoHowjp5F0Myv4T6yE8fn/0SztaFPHIXqsqMdG7SlKBiz5x6dodOOPn0CnoYjcOxXgsGE\n9dpHcG57C3fJNt91jGPm4j68Fc3ejj55DJZ5d6F2tWL/9DnU5iqUsHgs876LPnZ44D8EMeid9yRt\nvb3m7ty5c3n++efPqqpHEr/oTZrbCZqKYjw+0EpTPeC0obY30PX2I377G4ZNwjzvu+Bx4S7fg/3T\nv/hvz56Le/8qvzZd7HCsVz8ELjtKULDfNtXejhIUIjX8os+cdzmnrLkrBhvF0H3AoaLTgzkEbG3d\nDzCY0NobUO0doDd2P9ZkBp3ebw1fxRDkPedJSR9AZw49vzcgxHnolzV3V61a9cU7CdFP9JFJGDKm\n4z50dMEUowU8bjpffwAAJTwRXexwX+mmEhyFadxlKIBz13veY3QGTBOu7IfohfhisuauEKegaZq3\n4qajESUkGtvKJ/22G8dfgSE+C81t966sZfL+EvbUFuNprsSQkoMuJLo/QhcC6IWunuTkZO64445+\nXXNXiEBSFMW38Lm7LL/bdq2r5dSjcuMz0cdn9nl8QpyPHiV+m80ma+6KIUuflI1ijUDravG1KdYI\nOl79GbjsGMfOJWji1f0YoRBnR9bcFaIH1NZanLve95ZmpozFsf7ffgPBzPPuwpgxtR8jFMLfeXf1\nABw6dIgPPviAxsZGHn74YQ4fPozT6WT06NG9FqgQFypdeDzmS74BeNfcPXn0r6f6gCR+MWD0qEzn\n/fff55ZbbqG2tpZly5YB0NnZyW9+85s+DU6IC5HuFAOulJBo7Btewb7+33iaKvshKiF6rkd3/H/6\n05/4v//7P0aPHs37778PwOjRozlw4MAXHCnE4KOPSiHooltxbH8b3E4MmTNw7lwBLhsArsLPCf7y\n477594W40PQo8Tc1NTFq1CgA30hDRVFk1KEYskw58zGOnQeahmvfKtyF645vdDtwFW8iaOJV/Reg\nEGfQo66esWPH8s477/i1rVy5ktzc3D4JSogLieZx4S7fjafusF+7WluMp2ofmLqPZlfMMqmguHD1\nqKrn0KFDfOtb3yIlJYX8/HymTZtGSUkJ//jHPxg2bFgAwpSqHtE/1K4Wut75JVp7PQCGEVMwz/se\ntg+e8q2nq4QnoBjNqA1HANBFpWK96ue+QV1C9IfznqQNvLX8q1evpqqqisTERC699FKCg7vPQdJX\nJPGL/uDY8ibO/BV+baYZN+Pc+Ipfm3Hy9RjiRoDmQZ881jtHjxD9qFfKOS0WC1dccUWvBSXEQKDZ\nu0/YpnU0dN/R0YEhZWwAIhLi/J028d988809enj78ssv92pAQlxIDCNn+tXtK8FRmHIvx128Ce3Y\nLJ46PcasGf0YpRBn57RdPW+//XaPTnDttdf2akCnI109or+4qwtxFX6GYg7BlLMAXUg0alsdzoKP\nweXAOPoSmZ9HXHB6pY+/v0niF0KInuuVPn4hhip3RYH3jj8oGFPuInRhcXhaqnDt/gjNbcc4+lIM\nSTJ1iRg45I5fiDNwV+3HtuJJji20rljCsV7zMJ1vPQyOTu9Oig7r1Q+hjxvRf4EKcZIz3fH3zpJa\nQgxS7oMbOZb0ATRbK849Hx5P+gCaiqt4U+CDE+IcSeIX4gwUa3i3Nl1YbI/2E+JCddo+/qeffrpH\nJ5AVuMRgZsxZgPvwVtRW7wJEhqyLMI6dj6fqAO4j2wHvSF1T9qX9GKUQZ+e0iV9W2hICdJYwrDf8\nEk9NEYo5BH1UKgCWy+7G01CK5rKjT8hCUeTHsxg45OGuEEIMQr1WztnR0UFzc7NfW2pq6rlHJoQQ\nIuB6lPiLi4u59957OXDgAIqioGmabzqH/fv392mAQgghelePEv+jjz7KtGnT+Ne//sW8efNYtWoV\nv//975kwYUKPL3TXXXdRUVGBTqfDarXyv//7v2RnZ59z4EIIIc5Nj/r4p0yZwoYNGzAajUyePJlt\n27bR1dXF4sWLWbVqVY8u1N7eTmhoKACffPIJzz33XI/nAwLp4xcXFk9DKc5d76G57JjGzMGQltff\nIQnh57z7+IOCgnC73RiNRiIjI6mqqiIsLIyWlpYeB3Es6YP3WYEs2ygGKtXWRtfy3/jW2LWV7cZy\n1QMYEkb2c2RC9EyPEv+kSZN4//33ue6661i4cCF33nknJpOJ6dOnn9XFHnzwQdavX4+mafztb387\np4CF6G+e8j2+pO+l4T68VRK/GDDOupxTVVWWL19OZ2cn1157LRbL2S8vt2zZMlauXMmLL7541scK\n0d9spXup/s/Dfm1R879OxDRZXF0MDD1K/H//+9/51re+1a39pZde4vbbbz+nC+fm5rJ27VoiIyN7\ntL/08YsLiW3N33AXfQ6ALj4T6+U/kTV2xQXlvOfjnzhxIjt27OjWPnXqVLZs2fKFAXR2dtLW1kZi\nYiIAq1at4he/+AXr1q3rcV+/JH5xoVFba9HcDvTRaf0dihDdnPPD3Y0bNwLe7p1NmzZx4ndERUVF\njxdbt9ls3HPPPdhsNnQ6HeHh4Tz//PPygFcMaLrw+P4OQYhzcsY7/rlz5wJQXV3tu1sHUBSFmJgY\nvv3tbzNv3ry+jxK54xdCiLNx3l09P/3pT3nyySd7PbCzIYlfCCF6rlfW3HW5XOzatYu6ujquuOIK\nurq6ALBarb0X6RlI4hdCiJ477wFchYWFfO9738NkMlFbW8sVV1zB1q1befvtt3nqqad6NVghhBB9\nq0eTiD/yyCP88Ic/5IMPPsBg8H5XTJkyhe3bt/dpcEIIIXpfjxJ/cXExV199NYCvEsdqteJwOPou\nMiGEEH2iR4k/OTmZgoICv7bdu3eTlib1y0IIMdD0qI//nnvu4Tvf+Q433XQTLpeLv/71r7z66qs8\n/vjjfR2fEEKIXtbjqp59+/bx+uuvU1VVRUJCAl/5ylfIycnp6/h8pKpHCCF6rlfKOfubJH4hhOi5\n8y7ndDqd/OUvf2HlypXU1dURFxfHFVdcwfe+9z2CgoJ6NVghhBB9q0eJ/5FHHqGkpIQHH3yQ5ORk\nKisr+etf/0ptbS2//vWv+zpGIYQQvahHif/TTz/l448/JiwsDIDMzEzGjx/PZZdd1qfBCSGE6H09\nKueMiYnBZrP5tTkcDmJjY/skKCGEEH2nR3f8V199NXfccQe33XYb8fHx1NTU8PLLL3P11Vf7pm4G\nmDFjRp8FKoQQonf0qKrn2PTMZzyRovDpp5/2SlCnIlU9QgjRc1LOKYQQQ8yZEn+P+viFEEIMHpL4\nhRBiiJHEL4QQQ4wkfiGEGGIk8QshxBAjiV8IIYYYSfxCCDHESOIXQoghpkdTNpyv5uZmfvrTn1JW\nVobJZCI9PZ3HHnuMqKioQFxeCCHECQJyx68oCnfccQcffvghy5cvJzU1ld/97neBuLQQQoiTBCTx\nR0REMG3aNN/rvLw8qqqqAnFpIYQQJwl4H7+qqixdurRHE78JIYTofQHp4z/R448/jtVq5dZbbz2r\n40432dBAUVnfQUOzjTEjojAa9AC0djg4VNFKRko44SGyhKUQIjACmviXLFlCaWkpzz//PDrd2f3Y\nGMizc76xupj3N5cBEBkaxE9vnkBlfSfPv7MXt0fFoNfx3avHMnGkLGwjhOgd573Yem/4wx/+QEFB\nAS+88AImkylQl+13Da02Pjia9AGa2x2s3FjKgdJm3B4VALdH5bVVByXxCyECIiCJ/+DBg/z1r39l\n2LBh3HTTTQCkpKTw3HPPBeLy/aqt08XJv1NaO5y0dTq7tQkhRCAEJPFnZWVRWFgYiEtdcIYlhpIY\nbaW6scvXdlFOAlFhQazNr/JrE0KIQJAVuAKgpcPBB5vLaGqzMzU7nsmj43B7VD7eVk5xRSuZKeEs\nmJyKQS8DqYUQvUOWXhRCiCHmgni4O5R02d18sq2cmuYuJmbFMnl0HJqm8dnuavaXNpMeH8q8SSkY\nDV98h7/1QB07D9aTEGll/uRUrGYDJdVtrM2vwmjQMX9SCvFR1gC8KyHEYCF3/H3gNy/voKi8xff6\nG5ePpqnNzrvrj/japo+N59tXjj3jedbmV/LPD44/GxmZGsGtl43ksf/b5qsICrEY+eWd0wi1Dp1K\nKSHEF5PF1gOorrnLL+kDfLa7is92V/u1bdlXh9PlOeO5Pt/jf0xReQurdlT6kj5Ah81F/sGG84xa\nCDGUSOI/qq3LybYDdVQ2dPraXG6V/OIGCsua6ekPI0uQAb1O8WsLtZgItRhP2k9Pc4eDrQfqaGi1\n+dptDjfbC+spqW4j1OJ/F6/XKUSEdL+zD7Eau7VpmkZhWTP5xQ243Me/KCobOtl2oI72ruPlo22d\nTrYeqKO6sbPbeYQQg4/08eO9k/7D6/k4Xd4Eed0lI7hkfBK/+vd26lq8STlnRBT/c8N4dIpyplMR\najXxpRnpvm4da5CBq2YOo73LxbNv7cHlVlEUmDgylgdf2IyqaegUhTsWZ5MaH8qSl3fQYXMBMHlU\nLNYgA10ONwBfmpHO/EkpbD1QR2W9N0mPGRZJbka0XwyqpvHUG7soONwEQFyEhZ/fNol1u6p4a91h\nAExGHT/+Sh5uj8qf3tyN8+iXw1fmZLJoWtr5fqRCiAuY9PEDT76ygwNlx7tnjAYdl01OZeWmUr/9\nfnJjHmOH92wNgaqGTmqbuxiVGonV7P1+bet0UlzZSlpcCL95ZQdNbQ7f/lFhQYxKjWTj3hq/8zxy\n+xQa2+zER1pJigkGwKOqHChtwWjQkZUSjnLSl1FBSSN/eG2XX9uXpqfz0bZyv7v/0WkRuDwqhyrb\nfG1BRj1P/3AmJqO+R+9TCHFhGjJVPU6nB70e9PqzS1qddrffa5dbpc3WfSRtp92FR1XRKYpfslU1\nDTTvB31MUkwwcZEWv9r8sGATuRnRGPQ6Om3uk87tptPu6nZNVdMYNyLa7zx6nY7s9EhQ8ItD0zRU\nTaPrpPcD0G5z+SV98FYfuTz+bU6XB5dHPW3i93g8eDxgMskXgxAD1aBI/Dani/ue2+jrEslICuPB\nr03u8fGXjE/i5Y+LfK/HZ0Qzd0IKG/bU4Dn6KyM82MTOg/W8uHwfIRYjX5mTyYycBD7aUsa764/g\n9qjMmZjMV+Zksr+0mX9+cICGFjvjMqK588ox2B0eXly+l6KKVlJig8nLjGHz/trjMeQmMSotgt2H\nGn1tKbHBvL3uMAWHm4iNsPC1RaPITo/k9dXFrN5RiUGv46qLh3HZ1DQ2FtTw2upiOm0uJo+OJTzY\nROvRaSH0OoU5E5Jp7XCw64TzzxqfhMut8vrqYl/bpFGxBJu7PzMA+OW/tnGoyvvrwBpk4Lffn4HF\ndOp9hRAXrkHR1fPo/22htKbDr+2OL2Vz0bjEHp9/64E6dhc3kBQbzNyJKQQZ9ZRUt/HZ7mrMJj16\nncLKjce7fvQ6hR9cN46n39ztf93F2bz6abGvnx7g0gnJNLfZ/ZJuQpSFy6am+UbuXpKbhE6nUFDS\nyJb9dUSHmWlotbP+hMqeEIuRm+Zl8rcV+/2u+T835PLMf/f4vqTA+zzAo2rYnR5m5SYyPDEMh8vD\nqh0VVNV3kpsZw5TRcQBs3ldLweFGUuJCmDsx2Tdt9Ik27Knmbyv9r5ueEMIvvjG1x5+xECJwBn1X\nT22TrVvbpv21Z5X4p4yO8yXCY4YnhjE8MQyAvywr8NvmUTV2FXcvo9x/pNkv6QOUVLXR3G73a6tp\nsjEtO55L85L92nOGR5Mz3Puw9tGXtvpt67C52H+kuds18w82+CV9gLpmG9+7JsevLcio5/Jp6d2O\nnzYmnmlj4ru1n2jTCb9OjjnV5y6EuPANisSfFhdCUUWrX9ucvGSqGzv5YHMZXQ43s3KTyM2Ipsvu\n5v3NpZTXdTBuRDRzJiajAGt2VrL7UCNJMcFcMSOdYLORvSVNrM2vxGwyEB9l8Tu/Qa9j2ph41uZX\n+c2+OT4rhr1Hmmg5YbbNUWkRNLXZ2VZYfzzm+BA+3V5BcWUrmcnhLJyahtGgY9O+GrburyMq1Ex6\nQiilte2+YyJCTIzPimF9wfEHwAowdUw8n++p8avvj4+y8o+V+7E73czOS2bs8Cg67S7e21hKVUMn\nuRnRXDohGQ1YvaOSPYcbSY0L4fJp6VjNBnYfauSz3VVYgwwsmpbGnLxkX5XQiZ+7EGLgGRSJ/9pZ\nw1myNN/3WqfzJtbH/rmN9i7v3feOwnru/eoE3t9USkGJN4HtPtRIh82FQa/w37XeMsddhxopqW7j\nuksy+MPr+RzrCLMG6Zk3KZnN++oICzbx5UszGJUWyTe/lM2760twulXmT0ph8qg4okLNvPxxEbVN\nXUzIiuHaWSNwuDyoGuwvbSI9PpRgi9FXWrn7UCMNrTZGpUby4op9vvcRF2nhopwE8g82EB9l5ZYF\nIxmRFMb1s0fwyfYKTAYdV108nNFpkdx1bQ5vrjlEW6eTqdlxrNpeTpfDO0Bse1E9D9wyibfWHfJV\nL+061IjN6cHlVnnn8xJfHKW17Vw+LZ2n39jl+0LLL27gvq9O6Pa5T8iK6aW/oBAikAZFH//LHxXx\n6Y4Kv7b5k1L4ZLt/20U5CWwo8C+XjI+0YDDofHXxx8zMSeTzAv+Rs9++cgzTx/bO9Mnf+d0avyob\nk0HHyLSIbnfVD31tMiOSws7q3Jv21vDC8n1+bTPHJXYbCZwSG4zLrVLb7N9lc6rPKTcjit2H/GNL\nignmiTumnVVsQojAGPRTNkSEdh/NmhDdfeKyqDAzliD/HzmRoUFEnrTebZBRT3RE9zVwg0x61u+p\nZs/hRm8JJ97Vs3YU1bN5Xy0O5/EpGIrKW/hsVxXN7cdr9Wubuli3q4rSmvZu14wI6R7HsUrNz3ZV\n+U0D4XB62Lyvlh1F9b7uHVXT2HO4kfV7qgk6RalldHgQQSeVaEaEBBEZ6n9NS5CBqDBzt+MTo4O7\ntYUHy/xAQgxEg6KrZ86EZLYeqKOs1lvZM31MPHMnplBS3cb6Pd4715TYYC6bkkpMuJl/f1iIR9UI\nNhu4fnYGer3CkZp2Omwu9DqFG+ZkMH1MPDsPNvjOOT4zmpfeO+B7cJubEc0PrhvHr/+znZJqbz98\nTLiZh74+mRXrj/h+bRgNOn5yYx5tnU6ef2ev7wtj5rhEWjocON0qJoOOm+ZnkRQTzL4jzTS22VGA\nGWMSWPLKDt8vg/mTUlh88TCe+Oc2Glq9D4uHJ4bywK2TePatPb5S0BCLkfGZ0ewq9r5Oiw9hweRU\nQq0mln5yEI+qEWIxct3sEXg83lG+nXY3ep3CjXMzmTgylvyD9VQc/RV08bgEbpybxY6ieupb7L73\n9fVFo/rujyqE6DODoqsHvIOXDle1YTbpSY49/vOmqqGTLrubEclhvukWWjscVDV2MSIxzHd37HB5\nOFzVRkKU1XcXfOI5V++sZNWOSr9rXn/JCP57tJ/+mMUXDWPlxiOc+KnmjIiiuc3hNw+Q2aTn19+Z\nTlV9J2kJob7aebdH5VBlK1Fh3i+oY88jAHSKwuXT0/zKSsE7xcRbJ8Uxd2IycyYkY3d6GJEU5hvo\n1dzuoKapixFJYb5fAA6nh8PVbSRFWwk/+qtD1TQOV7ZhNRt8I4YBdh6sp63Dyczxieh1g+IHoxCD\n0qAv5wTvCNaM5PBu7ScmrWPCQ4J8Ce6YIKPeOxr2NOd0nGImzWMDxk5kc7g4+avU6fR0O97lVrGY\n9KTGh2I9ofvJoNeRGheCyajvdoyqadidp7pm9zaHy+P3BXhMZGj37p0gU/f3rlMUMlO6f54TsmRB\neCEGukGT+Pva7LxkNu2t9dXLJ8cEs2haOpv21fr68YNMeuZPTqW+xe43AnfOxBSa2x1+I2TzsmJ4\n5KVt1DR1kRBl5btXjyUm3Mzz7+yloKSJEIuRKdlxHDyhTDU3I5r5k1L5fE+N73lCZGgQi6als/tQ\no+8XhV6nMPuk8QFCCHHMoOnqCYTSmnY27ashzGrikrwkgs1GWjocrMuvwulWmZmbSEKUFZfbw2e7\nq6lp6mJCVqzvbnpnUT37jq7A9en2ckprj482HpYQyui0SD7YUuZrM+h1fPfqsRwoayYhysqs3ESM\nBj01TV18vrsak0HHJXlJRIQE0Wl3sS6/irYuJ9PHJJCeEBrwz0cIceGQNXcvQHc+udpvtK1epzAq\nLYJ9J43MfeDWiWSlRAQ6PCHEADck+vgvdC63ysqNR7xr7iaEdkvyY4dHMSrVvy3EYiQ9Xu7chRC9\nSxJ/gLy+uphPj5Z4HqxoJTs9kimj43xTNty8YCQhFgOddjdb9tcSFWbmhjkZMi++EKLXBaSrZ8mS\nJXz44YdUVlayfPlyRo4cedbnGOhdPT969nNaT5i/RwH+/OPZpxxsJYQQ56vfR+7OmzePl19+meTk\noVtpEhvuP8lbeIiJ8rp2PtxSxqHK1tMcJYQQvS8gXT2TJ/d8UZTB6sZ5mTzz5m7aulwEmfSMGxHN\nr/6zw7f9q/OzWDA5tR8jFEIMFdLHHyAZSeH89q6LqWzoID7Syv1/3ei3feWGI5L4hRABMWAS/+n6\nqgaapETvaNiTn6yoGsTGSgWPEKLvDZjEP9Af7p5sweQU3v6sxO91fX37GY4QQoiekzr+C9CVFw8n\nPSHUV86ZmyGLmgghAiMg5ZxPPPEEH330EQ0NDURGRhIREcHKlSvP6hyD7Y5fCCH6kkzZIIQQQ0y/\n1/ELIYS4cEjiF0KIIUYSvxBCDDGS+IUQYogZMOWcOp3S3yEIIcSAcaacOWCqeoQQQvQO6eoRQogh\nRhK/EEIMMZL4hRBiiJHEL4QQQ4wkfiGEGGIk8QshxBAjiV8IIYYYSfxCCDHESOIXQoghRhJ/gJSU\nlHDjjTeycOFCbrzxRo4cOdJtH4/Hw6OPPsr8+fNZsGABb7zxRuADFd0sWbKEuXPnMmrUKIqKik65\nj/ztLkzNzc3ceeedLFy4kCuvvJIf/OAHNDU1ddvPZrPxP//zPyxYsIBFixaxevXqfog2gDQRELfd\ndpu2bNkyTdM0bdmyZdptt93WbZ+3335b++Y3v6l5PB6tsbFRmzVrllZeXh7oUMVJtm7dqlVVVWlz\n5szRCgsLT7mP/O0uTM3NzdqmTZt8r3/zm99oDzzwQLf9nnnmGe3BBx/UNE3TSkpKtIsuukjr6OgI\nWJyBJnf8AdDY2Mi+fftYvHgxAIsXL2bfvn3d7jzee+89brjhBnQ6HVFRUcyfP58PPvigP0IWJ5g8\neTKJiYln3Ef+dhemiIgIpk2b5nudl5dHVVVVt/3ef/99brzxRgCGDRtGTk4O69atC1icgSaJPwCq\nq6uJj49Hr9cDoNfrVYSYWgAABQhJREFUiYuLo7q6utt+SUlJvteJiYnU1NQENFZxbuRvd+FTVZWl\nS5cyd+7cbtuqqqpITk72vR7sfz9J/EKIIeHxxx/HarVy66239nco/U4SfwAkJiZSW1uLx+MBvA8C\n6+rqunUfJCYm+v0Mra6uJiEhIaCxinMjf7sL25IlSygtLeWpp55Cp+ue9pKSkqisrPS9Hux/P0n8\nARAdHU12djYrVqwAYMWKFWRnZxMVFeW336JFi3jjjTdQVZWmpiY++eQTFi5c2B8hi7Mkf7sL1x/+\n8AcKCgp47rnnMJlMp9xn0aJFvPbaawAcOXKEPXv2MGvWrECGGVCyEEuAHDp0iPvvv5+2tjbCwsJY\nsmQJI0aM4M477+SHP/wh48aNw+Px8Nhjj7F+/XoA7rzzTt8DJ9F/nnjiCT766CMaGhqIjIwkIiKC\nlStXyt9uADh48CCLFy9m2LBhmM1mAFJSUnjuuee4+uqreeGFF4iPj6erq4v777+f/fv3o9PpuO++\n+5g/f34/R993JPELIcQQI109QggxxEjiF0KIIUYSvxBCDDGS+IUQYoiRxC+EEEOMJH4hhBhiJPGL\nIWvu3Lls2LChX659//3388c//rFfri2EJH4hzsGx6TeEGIhkAJcYku677z6WL1+OyWRCr9dz1113\nsWfPHrZv347dbmf06NE88sgjZGVlAd479KCgIKqqqti6dSt//vOfyc7O5oEHHmDLli0MHz6cmTNn\nsmXLFpYuXQp4R2s/8cQT7N27l/9v7/5BWoeiMIB/1VgQ6lB18c8iODmJpjpoi6UUwUIRdHB2cBCK\nBUE3B3ERpS6CXaSztIMiiAiCi5tTQCjUgKCCiFQkxKqxHAclvD7esw/RFyHfb0pyc5N7MhzCvSHH\n7/djZmYGIyMj2NrawuLiIjweD+rq6tDf3490Ou3k4yC3cbIYAJGTwuGwHB8f2/vZbFYMw5CnpydZ\nWlqSeDxut83Pz0tPT4+cnJxIuVyWx8dHSSaTkkwm5eHhQQqFgoRCIZmYmBAREdM0JRQKSS6XE8uy\n5PT0VPr6+qRQKNjXS6VS/zdgonec6iF6Nz4+Dp/PB6/Xi0QigXw+D8Mw7PZIJILe3l7U1NRAURQc\nHBwgkUigvr4enZ2dGB0dtc89OjpCW1sbxsbGoCgKurq6MDw8zOIs9CMoTg+A6Ccol8tYW1vD/v4+\nisWi/eveu7s7NDQ0AEDFb7SLxSJeXl4qjv26fXV1BU3ToKpqxT3i8fh3h0JUFRM/EYDd3V0cHh4i\nk8mgvb0dhmEgEAhA/rIE1tjYCEVRcH19jY6ODgCoqKjW0tKCQCCATCbzx/4ej+frgyD6R5zqIddq\nbm7GxcUFAMA0TXi9Xvj9fpRKJaRSqQ/71tbWIhqNYn19HaVSCbquY2dnx24fGhrC+fk5tre3YVkW\nLMuCpmnQdR3AW42Gy8vL7wuO6ANM/ORaU1NT2NjYgKqquL+/R2trK4LBIGKxGLq7u6v2X1hYgGEY\nGBgYwNzcHGKxmF3ow+fzYXNzE3t7ewgGgxgcHMTq6iqen58BvK0nnJ2dQVVVTE9Pf2ucRL/j55xE\nX2RlZQW3t7dYXl52eihEH+IbP9En6bqOfD4PEYGmacjlcohGo04Pi6gqLu4SfZJpmpidncXNzQ2a\nmpowOTmJSCTi9LCIquJUDxGRy3Cqh4jIZZj4iYhchomfiMhlmPiJiFyGiZ+IyGWY+ImIXOYVFOTC\nNiU14s0AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "sBrca77tWenX",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def ecdf(data):\n",
        "  \"\"\"Compute ECDF fro a one-dimensional array of measurements.\"\"\"\n",
        "  n = len(data)\n",
        "  x = np.sort(data)\n",
        "  y = np.arange(1, n+1) / n\n",
        "  return x, y\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RnV2HHu1WekX",
        "colab_type": "code",
        "outputId": "0325aa15-31c7-4dfd-8890-b16e90f4c4bc",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "source": [
        "x_vers, y_vers = ecdf(versicolor_petal_length)\n",
        "\n",
        "plt.plot(x_vers, y_vers, marker='.', linestyle='none')\n",
        "plt.margins(0.02)\n",
        "\n",
        "plt.xlabel('petal length (cm)')\n",
        "plt.ylabel('ECDF');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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VVQgICMDw4cMxdepU3pODXB7nYRBJY7FwLF++HIsXL8bcuXMB3Fgtd/z48abts2bNwurV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\niCT5f8FUFJOG+bCjAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "EG669HWDWehb",
        "colab_type": "code",
        "outputId": "d78234da-2bca-418b-d583-02551276d38d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "x_set, y_set = ecdf(setosa_petal_length)\n",
        "x_vers, y_vers = ecdf(versicolor_petal_length)\n",
        "x_virg, y_virg = ecdf(virginica_petal_length)\n",
        "\n",
        "plt.plot(x_set, y_set, marker='.', linestyle='none')\n",
        "plt.plot(x_vers, y_vers, marker='.', linestyle='none')\n",
        "plt.plot(x_virg, y_virg, marker='.', linestyle='none')\n",
        "\n",
        "plt.legend(('setosa', 'versicolor', 'virginica'), loc='lower right');\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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AimpcsMzBX9N/CAJvTVdELOOIJZNPCI3HfQOmUFTjR1w2+fDwcCQmJqKgoAAAUFBQgMTE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\nIUTBqMkTQoiC/X9WFZgFMKfUZwAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5CJ3rgQ1lYx-",
        "colab_type": "code",
        "outputId": "7cc2c20b-5fa3-4dea-b924-0592cbb090ba",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "mean_length_vers = np.mean(versicolor_petal_length)\n",
        "print(f'I. versicolor: {mean_length_vers} cm')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "I. versicolor: 5.936 cm\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IO2QLJEFlYvD",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "percentiles = np.array([2.5, 25, 50, 75, 97.5])\n",
        "ptiles_vers = np.percentile(versicolor_petal_length, percentiles)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MvRl9nv3lYsR",
        "colab_type": "code",
        "outputId": "547f1261-b8ff-434a-8b61-2f96c66b8624",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "source": [
        "plt.plot(x_vers, y_vers, '.')\n",
        "plt.xlabel('petal length (cm)')\n",
        "plt.ylabel('ECDF')\n",
        "plt.plot(ptiles_vers, percentiles / 100, marker='D', color='red', linestyle='none');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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8R23h62jWjg/d0NLSgpycHDz00EMdjtn6M8Q7iW5Yvnw5RFHEuHHj8MILL+CW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\niIjIrP8P7cLHWP2pJ/YAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9dbwjdYElYpq",
        "colab_type": "code",
        "outputId": "409c7230-e630-497b-e31f-ad3695279b55",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "source": [
        "sns.boxplot(x='target', y='petal length (cm)', data=iris_df);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ne/fulcvlkmEY1Zdz2LNnT0ADAg1VUVGhli59UQ8++IgiI6PsjgOYZuoErtmzZ6tXr17a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\nP6g7gn6RzGZAAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M201284iNZ3q",
        "colab_type": "text"
      },
      "source": [
        "## Computing variance"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ikCPHSX3NY4Q",
        "colab_type": "code",
        "outputId": "68679103-fe90-4b7e-a7df-f09b456c346c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "differences = versicolor_petal_length - np.mean(versicolor_petal_length)\n",
        "diff_sq = differences ** 2\n",
        "variance_explicit = np.mean(diff_sq)\n",
        "variance_np = np.var(versicolor_petal_length)\n",
        "\n",
        "variance_explicit, variance_np"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "(0.261104, 0.261104)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 107
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zxRu1dmMNY0y",
        "colab_type": "code",
        "outputId": "0de06007-5d6a-4282-a016-70f6fe12267f",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "source": [
        "plt.plot(versicolor_petal_length, versicolor_petal_width, marker='.', linestyle='none')\n",
        "plt.xlabel('Petal length')\n",
        "plt.ylabel('Petal width');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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PH96zqUvyKI7uQ84+V1x5jqnx/KwbU7QAcMOYskLi4YcfbrIBpVy6dAlFRUWYOXMmAOCX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\nRQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "pDIeIX-dNYx7",
        "colab_type": "code",
        "outputId": "9a78b5a2-5309-4571-8e30-20301d0fe0ca",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        }
      },
      "source": [
        "covariance_matrix = np.cov(versicolor_petal_length, versicolor_petal_width)\n",
        "print(covariance_matrix)\n",
        "\n",
        "petal_cov = covariance_matrix[0,1]\n",
        "print(petal_cov)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "[[0.26643265 0.05577959]\n",
            " [0.05577959 0.03910612]]\n",
            "0.05577959183673469\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Nq3bZR2NlYmG",
        "colab_type": "code",
        "outputId": "24191642-5fdc-45ca-afd8-d5790253f111",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "def pearson(x, y):\n",
        "  corr_mat = np.corrcoef(x, y)\n",
        "  return corr_mat[0, 1]\n",
        "\n",
        "r = pearson(versicolor_petal_length, versicolor_petal_width)\n",
        "\n",
        "print(r)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.5464610715986299\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "ACaMjwcpmhGo",
        "colab_type": "text"
      },
      "source": [
        "## Thinking probabilistically-- Continuous variables"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5i3tK8Iqmg4y",
        "colab_type": "code",
        "outputId": "d6487ecd-7c78-4cf9-9c0b-5b4af281bedf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "np.random.seed(42)\n",
        "\n",
        "sim_size = 100000\n",
        "\n",
        "random_numbers = np.empty(sim_size)\n",
        "for i in range(sim_size):\n",
        "  random_numbers[i] = np.random.random()\n",
        "\n",
        "plt.hist(random_numbers);"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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EAMCKSAAArAouEtlcPDCVSmnz5s26/fbbdccdd6izs9P9ieZRNmveuXOn7rrrLjU0NOje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\nSAAArIgEAMDqfwGEVppZOqOvoQAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9VKlarGsmg3R",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def perform_bernoulli_trials(n, p):\n",
        "  n_success = 0\n",
        "  trials = np.random.random(n)\n",
        "  success = trials < p\n",
        "  return success.sum()\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bxHxXasGmgzv",
        "colab_type": "code",
        "outputId": "9c118185-fd32-4951-8122-3cf0fe811bb3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "perform_bernoulli_trials(3, 0.5)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "1"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 113
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7IQm4Ve2mgwL",
        "colab_type": "code",
        "outputId": "ecdc995b-bc5b-4bcc-f70a-f5e3f7470890",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 376
        }
      },
      "source": [
        "np.random.seed(42)\n",
        "n_defaults = np.array([perform_bernoulli_trials(100, 0.05) for _ in range(1000)])\n",
        "plt.hist(n_defaults, normed=True)\n",
        "plt.xlabel('number of defaults our of 100 loans')\n",
        "plt.ylabel('probability')"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:3: MatplotlibDeprecationWarning: \n",
            "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
            "  This is separate from the ipykernel package so we can avoid doing imports until\n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0, 0.5, 'probability')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 114
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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Ozg6FhYXo2bMnVqxYARcXl1qn79ixY7W/3di4caP+tkajwZEjR6qdXqVSISoqSmpcasSa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\nIiJZWCBERCTL/wMl2K3r+Q1PiAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JpUlG9PlmgQ1",
        "colab_type": "code",
        "outputId": "b009e859-d202-4896-e10f-643f1ed4a2fe",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "source": [
        "x, y = ecdf(n_defaults)\n",
        "plt.plot(x, y, marker='.', linestyle='none')\n",
        "plt.xlabel('num defaults')\n",
        "plt.ylabel('defaults prob.');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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JkKiS8PPzs3cOIiKSINEHromIqPVhSRARkSCWBBERCWpSSVy/fh03btywdRYiIpIYUSXx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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VdeAYj3PwEwg",
        "colab_type": "code",
        "outputId": "8e3b18ab-3c66-4ed5-c903-0c7fc32f95e3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "np.sum(n_defaults >= 10) / len(n_defaults)\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.022"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 116
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "faK8QSLRwEpl",
        "colab_type": "code",
        "outputId": "89c95ea0-7b2a-4436-d2d4-df2ac4bff761",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "np.random.binomial(4, 0.5, size=10)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([2, 2, 2, 2, 2, 2, 3, 3, 2, 2])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 117
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ljY7nYW3wElV",
        "colab_type": "code",
        "outputId": "0b22be4e-0a7e-4f67-eb1d-4c6d370f9ac8",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 285
        }
      },
      "source": [
        "np.random.seed(42)\n",
        "\n",
        "n_defaults = np.random.binomial(n=100, p=0.05, size=10000)\n",
        "x, y = ecdf(n_defaults)\n",
        "\n",
        "plt.plot(x, y, marker='.', linestyle='none')\n",
        "plt.xlabel('defaults %')\n",
        "plt.ylabel('CDF');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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JSYffr1mzxuf6s2bNCnQkAEAXOOMaAGCIkgAAGKIkAACGKAkAgCFKAgBgiJIAABiiJAAA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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ZwTclnhBwEjL",
        "colab_type": "code",
        "outputId": "4d258e50-5497-46b3-c2ca-c3bc3a6158f5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 358
        }
      },
      "source": [
        "bins = np.arange(0, max(n_defaults) + 1.5) - 0.5\n",
        "plt.hist(n_defaults, normed=True, bins=bins)\n",
        "plt.xlabel('defaults')\n",
        "plt.ylabel('PMF');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.6/dist-packages/ipykernel_launcher.py:2: MatplotlibDeprecationWarning: \n",
            "The 'normed' kwarg was deprecated in Matplotlib 2.1 and will be removed in 3.1. Use 'density' instead.\n",
            "  \n"
          ],
          "name": "stderr"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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3RNcnIiKT0KhnLp/yer20tbVRW1vL66+/zkMPPaTPNURE5JpGDZf33nuP2tpaXn31VebP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\nhYuIiBjufwHJZ/xx0qE3ggAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "mASiwjIawEfW",
        "colab_type": "code",
        "outputId": "fb8e02c8-8ce4-4bc3-9367-0022fd29a22e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "samples_poisson = np.random.poisson(10, 1000)\n",
        "np.sort(np.unique(samples_poisson))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([ 3,  4,  5,  6,  7,  8,  9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19,\n",
              "       20, 22])"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 123
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "yfVy1TufwEb8",
        "colab_type": "code",
        "outputId": "cc413db3-93de-44f2-a514-cc931a4f610c",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 54
        }
      },
      "source": [
        "stats.describe(samples_poisson)"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "DescribeResult(nobs=1000, minmax=(3, 22), mean=9.996, variance=10.29628028028028, skewness=0.34700785112511734, kurtosis=0.07712341949064827)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 127
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4AZD67xIwEYz",
        "colab_type": "code",
        "outputId": "f8285e4c-fcea-4080-9489-d75410f02b0b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 70
        }
      },
      "source": [
        "n = [20, 100, 1000]\n",
        "p = [0.5, 0.1, 0.01]\n",
        "for i in range(3):\n",
        "  samples_binomial = np.random.binomial(n[i], p[i], 10000)\n",
        "  print('n =', n[i], 'Binom:', np.mean(samples_binomial),\n",
        "                                 np.std(samples_binomial))"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "n = 20 Binom: 10.0 2.2187383802512635\n",
            "n = 100 Binom: 9.9896 3.002614167687883\n",
            "n = 1000 Binom: 9.966 3.1473868526128146\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "08ShGDTYwHly",
        "colab_type": "text"
      },
      "source": [
        "Was 2015 anomalous?\n",
        "1990 and 2015 featured the most no-hitters of any season of baseball (there were seven). Given that there are on average 251/115 no-hitters per season, what is the probability of having seven or more in a season?"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5SkCgkUDwF-k",
        "colab_type": "code",
        "outputId": "5795841d-682e-497e-babc-b9e0a98311f9",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 52
        }
      },
      "source": [
        "n_nohitters = np.random.poisson(251/115, size=10000)\n",
        "n_large = np.sum(n_nohitters >= 7)\n",
        "print(f'n_large: {n_large}')\n",
        "p_large = n_large / 10000\n",
        "print('Probability of seven or more no-hitters:', p_large, p_large * 100)\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "n_large: 68\n",
            "Probability of seven or more no-hitters: 0.0068 0.6799999999999999\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "9BDPQtR8wF7q",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "samples_std1 = np.random.normal(20, 1, 100000)\n",
        "samples_std3 = np.random.normal(20, 3, 100000)\n",
        "samples_std10 = np.random.normal(20, 10, 100000)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "WGMgdzJAwF5c",
        "colab_type": "code",
        "outputId": "0f2797af-cace-49be-e7c9-a78d95b3571a",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "plt.hist(samples_std1, bins=100, density=True, histtype='step')\n",
        "plt.hist(samples_std3, bins=100, density=True, histtype='step')\n",
        "plt.hist(samples_std10, bins=100, density=True, histtype='step');"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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KCgrQ2NgIv98Pr9eLo0ePwmw2h51GRESxF3aHLwBcunQJdrsd169fR2pqKmpq\napCdnY2ysjIsX74cubm5kCQJ69atw6lTpwAAZWVlsNlsABByGhERxZ6i8CciorsLd/gSEakQw5+I\nSIUY/kREKsTwJyJSIdWHf3V1NQoKCjBv3jwsWLAAFy5cCEz74osvUFpaCrPZjHnz5uH8+fNx7Gn8\ntLS0wGazwWw2w2azobW1Nd5diqtr166hrKwMZrMZhYWF+M1vfgOv1wsA+Nvf/oZ58+bBbDajtLQU\nHo8nzr2Nr1dffRUTJ07E3//+dwCsT6+bN2/C4XBgzpw5KCwsxNq1awHE+H9NVrljx47J33zzTeDx\n7NmzA9PsdrtcW1sry7Isf/jhh3J+fr7s9/vj0s94WrRokbx//35ZlmV5//798qJFi+Lco/i6du2a\n/Je//CXw/OWXX5ZfeOEFWZIkOS8vT/7www9lWZbl2tpa2W63x6ubcffxxx/Lixcvlp999ln5888/\nZ31us379ennDhg2BPOnq6pJlObb/a6oP/9t5vV75kUcekSVJkmVZlh977DHZ4/EEps+dO1c+f/58\nvLoXF1988YU8ZcoU+bvvvpNlWZa/++47ecqUKUF1UbtDhw7Jv/zlL+Xz58/Lc+fODbzu8Xjkxx57\nLI49i5+bN2/Kzz33nHzlypVA+LM+t/h8PnnKlCmyz+cLej3W/2uqH/a53ZtvvolnnnkGWq0W165d\ngyzLQWcyD+WCdCNdqAv7EeD3+/GnP/0Js2bN6nMBQ71eD7/fj+7u7jj2MD62bduGefPmBV22nfW5\n5cqVKxgzZgxeffVVFBcXY9GiRTh79mzM/9fu+jt5/exnPwu6rtDtTp8+HSj0wYMHceDAAbz55pux\n7B6NcOvXr8c999yDhQsX4siRI/HuTkI4d+4cPv74Y/zud7+Ld1cSkiRJuHLlCn784x9jzZo1OH/+\nPJYuXYpt27bFtB93ffj/+c9/DtvmyJEj+MMf/oBdu3bhRz/6EQAgLS0NAOD1egNb/2q8IN3tF/br\nvZ9Dfxf2U6Oamhr885//xI4dO6DVavtcwNDr9UKr1WLMmDFx7GXsffjhh7h06RJmz54NAGhvb8fi\nxYuxaNEi1ge3/qeSkpJgsVgAAI8++ijS0tKQkpIS0/811Q/7vPfee9i4cSN27tzZ585iBQUFeOut\ntwAAZ8+eRU9PDyZNmhSPbsaN0gv7qc3WrVvx8ccfo7a2Fj/4wQ8AAJMmTUJPTw/Onj0LAHjrrbcC\nNzBSk/Lycpw8eRLHjh3DsWPHMHbsWOzcuRNLlixhfXBruOvJJ58MXOuspaUFHo8HWVlZMf1fU/21\nfX7yk58gOTk5qMC7du1CWnsh0ZcAAACxSURBVFoaurq6sHr1arS1teGHP/whqqur8fjjj8ext/Ex\n0IX91OrixYuwWCzIyspCSsqtWzyOHz8etbW1+Otf/wqHw4GbN29i3Lhx2Lx5c+DXpFrNmjULO3bs\nwEMPPcT6/H9XrlzBiy++iO7ubiQlJWHFihX46U9/GtP/NdWHPxGRGql+2IeISI0Y/kREKsTwJyJS\nIYY/EZEKMfyJiFSI4U9EpEIMfyIiFWL4ExGp0P8DEYvdiKz03ZQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "k57UsFDKwF2F",
        "colab_type": "code",
        "outputId": "13a57ad7-1cf1-4c66-dd4c-d992902ca652",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 268
        }
      },
      "source": [
        "x_std1, y_std1 = ecdf(samples_std1)\n",
        "x_std3, y_std3 = ecdf(samples_std3)\n",
        "x_std10, y_std10 = ecdf(samples_std10)\n",
        "\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'), loc='lower right')\n",
        "plt.show();\n"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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d/H2f48HK0XCLo0pU7QpVGnEZ8NPfEQQjukZcBiUxDKittp1jiL8ciooVfET+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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}