Normal Distribution.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "source": [
    "# Normal Distribution Simulation"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import collections"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## RNG"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "source": [
    "class Die:\n",
    "    def __init__(self, sides : int):\n",
    "        self.sides = sides\n",
    "    \n",
    "    def roll(self):\n",
    "        return np.random.randint(6) + 1\n",
    "    \n",
    "    def rolls(self, iterations : int):\n",
    "        result = []\n",
    "        for i in range(iterations):\n",
    "            result.append(self.roll())\n",
    "            \n",
    "        return result\n",
    "    "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## RNG Processing"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "source": [
    "class DataGenerator:\n",
    "    \n",
    "    mean = 0\n",
    "    standard_deviation = 0\n",
    "    \n",
    "    def random_rolls(self, amount : int):\n",
    "        rolls = Die(6).rolls(amount)\n",
    "        rolls.sort()\n",
    "        self.mean = np.mean(rolls)\n",
    "        self.standard_deviation = np.std(rolls)\n",
    "        return rolls\n",
    "    \n",
    "    def random_rolls_mean(self, amount : int):\n",
    "        result = []\n",
    "\n",
    "        for i in range(10000):\n",
    "            rolls = Die(6).rolls(10)\n",
    "            mean = np.mean(rolls)\n",
    "            result.append(mean)\n",
    "            \n",
    "        result.sort()\n",
    "        self.mean = np.mean(result)\n",
    "        self.standard_deviation = np.std(result)\n",
    "        \n",
    "        return result\n",
    "    \n",
    "\n",
    "data_gen = DataGenerator()\n",
    "    \n",
    "result = data_gen.random_rolls_mean(1000)\n",
    "mean = data_gen.mean\n",
    "std = data_gen.standard_deviation\n",
    "        "
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Plotting"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "source": [
    "x = collections.Counter(result).keys()\n",
    "y = collections.Counter(result).values()"
   ],
   "outputs": [],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "source": [
    "plt.boxplot(x, vert=False, widths = 100)\n",
    "plt.plot(x,y)\n",
    "plt.show()"
   ],
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Mean & Standard Deviation"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "source": [
    "print(\"Mean : \" + str(mean) + \"\\n\" + \"Standard Deviation : \" + str(std))"
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "Mean : 3.5098199999999995\n",
      "Standard Deviation : 0.5425970582301382\n"
     ]
    }
   ],
   "metadata": {}
  },
  {
   "cell_type": "markdown",
   "source": [
    "## Confidence Interval"
   ],
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "source": [
    "# 95 percentile interval\n",
    "z_score = 1.96\n",
    "\n",
    "std_error = std/np.sqrt(len(result))\n",
    "\n",
    "start_of_range = std_error*-z_score + mean\n",
    "end_of_range = std_error*z_score + mean\n",
    "    \n",
    "print(\"If you roll a die 20 times, 95% of the time, their combined average will be between \" + str(np.around(start_of_range, 2)) + \" & \" + str(np.around(end_of_range ,3)) + \"!\")\n",
    "                                                                                                                                               \n",
    "                                                                                                                                               \n",
    "                                                                                                                                               "
   ],
   "outputs": [
    {
     "output_type": "stream",
     "name": "stdout",
     "text": [
      "If you roll a die 20 times, 95% of the time, their combined average will be between 3.5 & 3.52!\n"
     ]
    }
   ],
   "metadata": {}
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}