{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "X6QIH3eK6Hwd"
   },
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "tbfUwHym6vhs"
   },
   "outputs": [],
   "source": [
    "# list of all xs\n",
    "x = list(range(1, 11))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1166,
     "status": "ok",
     "timestamp": 1571315496557,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "C5oA9j5B7THl",
    "outputId": "45bb6609-a114-41b3-ea99-f7df75d02fa5"
   },
   "outputs": [],
   "source": [
    "print(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "RFRcEQHp9ZdC"
   },
   "outputs": [],
   "source": [
    "# pmf\n",
    "p_X_x = [1/len(x)] * len(x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 34
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1154,
     "status": "ok",
     "timestamp": 1571315496561,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "PSoAZpl99nLv",
    "outputId": "316a65df-1e28-4dd7-87ad-63fc33207efb"
   },
   "outputs": [],
   "source": [
    "# sums to \n",
    "print(p_X_x)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1649,
     "status": "ok",
     "timestamp": 1571315497065,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "qShRhhOn934X",
    "outputId": "b3f0f052-558e-4bdf-b294-218a980dd36b"
   },
   "outputs": [],
   "source": [
    "plt.bar(x, p_X_x)\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('P(X=x)')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "M72x9J89FnN8"
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "M2ssEju6Gg1A"
   },
   "outputs": [],
   "source": [
    "# range of xs\n",
    "x = np.linspace(-10, 10, 100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {},
    "colab_type": "code",
    "id": "q9ikfnk-HEhE"
   },
   "outputs": [],
   "source": [
    "# first normal distribution with mean = 0, variance = 1\n",
    "p_X_1 = stats.norm.pdf(x=x, loc=0.0, scale=1.0**2)\n",
    "\n",
    "# second normal distribution with mean = 0, variance = 2.25\n",
    "p_X_2 = stats.norm.pdf(x=x, loc=0.0, scale=1.5**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "colab": {
     "base_uri": "https://localhost:8080/",
     "height": 300
    },
    "colab_type": "code",
    "executionInfo": {
     "elapsed": 1234,
     "status": "ok",
     "timestamp": 1571315524484,
     "user": {
      "displayName": "Andrew Worsley",
      "photoUrl": "https://lh3.googleusercontent.com/a-/AAuE7mAp-Td-yKvu76Tg0Swzal8U17btuwNIXFmWVwZo=s64",
      "userId": "11337101975325054847"
     },
     "user_tz": -660
    },
    "id": "sYZ9BRflIJkE",
    "outputId": "ff365e43-a2c7-4b3b-dfdf-65ec397401e5"
   },
   "outputs": [],
   "source": [
    "plt.plot(x,p_X_1, color='blue')\n",
    "plt.plot(x, p_X_2, color='orange')\n",
    "plt.xlabel('X')\n",
    "plt.ylabel('P(X)')"
   ]
  }
 ],
 "metadata": {
  "colab": {
   "collapsed_sections": [],
   "name": "distributions.ipynb",
   "provenance": []
  },
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
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    "version": 3
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   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
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}