cbrow216.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython version:      %6.6s 8.3.0\n"
     ]
    }
   ],
   "source": [
    "import IPython\n",
    "import json\n",
    "# Numpy is a library for working with Arrays\n",
    "import numpy as np\n",
    "# SciPy implements many different numerical algorithms\n",
    "import scipy as sp\n",
    "# Pandas is good with data tables\n",
    "import pandas as pd\n",
    "# Module for plotting\n",
    "import matplotlib\n",
    "#BeautifulSoup parses HTML documents (once you get them via requests)\n",
    "import bs4\n",
    "# Nltk helps with some natural language tasks, like stemming\n",
    "import nltk\n",
    "# Bson is a binary format of json to be stored in databases\n",
    "import bson\n",
    "# Mongo is one of common nosql databases \n",
    "# it stores/searches json documents natively\n",
    "import pymongo\n",
    "print (\"IPython version:      %6.6s\", IPython.__version__)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Make a 2 row x 3 column array of random numbers\n",
      "[[0.99006716 0.40357118 0.63018366]\n",
      " [0.57035664 0.94245908 0.19480125]]\n",
      "Add 5 to every element\n",
      "[[5.99006716 5.40357118 5.63018366]\n",
      " [5.57035664 5.94245908 5.19480125]]\n",
      "Get the first row\n",
      "[5.99006716 5.40357118 5.63018366]\n"
     ]
    }
   ],
   "source": [
    "#Here is what numpy can do\\n\",\n",
    "print (\"Make a 2 row x 3 column array of random numbers\")\n",
    "x = np.random.random((2, 3))\n",
    "print (x)\n",
    "\n",
    "#array operation (as in R)\n",
    "print (\"Add 5 to every element\")\n",
    "x = x + 5\n",
    "print (x)\n",
    "\n",
    "# get a slice (first row) (as in R)\n",
    "print (\"Get the first row\")\n",
    "print (x[0, :])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<function ndarray.any>"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# IPython is quite modern: just press <TAB> at the end of the unfinished statement to see the documentation\n",
    "#       on possible completions.\n",
    "#       In the code cell below, type x.<TAB>, to find built-in operations for x\n",
    "x.any"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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+vKquWWD1FX+rg4PlS/Jq4OXAq6q7QDeOfIfKOORy4I+66Uk4hs9gcJ31q0l2dRluTfJL48h3kIxU1YNV9ZOqehj4Wx65bDAxGRmcTV7TXTr4MvAwgzfAmoTH+cD4KuAPgSuHVp+kY7gRODD9j4z5cR7JuC/6z/1gcKPiU8AHD7L8C/z0DdXn8NM3Ye5leW8SzZsPOB24C5iaM76i+RbIeOLQ9JuAq7vpM/npm0RfHudj3K2zi0duqK5ovgWO4Zqh6fMZXCOetMf5dcBfdNPPYnAZIZPyvdItOx344pyxSTqGO4AXd9OnAdvH9Vwc+d827gDzHOwXMriZcTtwW/dxBvAHDM5IHgIeBD4/tM2FDO6s3013h3sM+XZ230QHxj4+jnwLZPwMcEc3/k8MbrIeeIJ/pMv4NYZ+eK5kvjnr7OKRcl/RfAscw7/vMtzO4P2Shst+Uh7nI4F/6B7rW4GXjCPjoR5n4JPA6+bZZlKO4QuB7Qx+2GwDfmNcz8VRP3z7AUlq0ERec5ck9WO5S1KDLHdJapDlLkkNstwlqUGWuyQ1yHKXpAb9Pz/CSmSaQFZTAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "import matplotlib.pyplot as plt\n",
    "heads = np.random.binomial(500, .5, size=500)\n",
    "histogram = plt.hist(heads, bins=10)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "# Task 1\n",
    "## write a program to produce Fibonacci numbers up to 1000000"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0\n",
      "1\n",
      "1\n",
      "2\n",
      "3\n",
      "5\n",
      "8\n",
      "13\n",
      "21\n",
      "34\n",
      "55\n",
      "89\n",
      "144\n",
      "233\n",
      "377\n",
      "610\n",
      "987\n",
      "1597\n",
      "2584\n",
      "4181\n",
      "6765\n",
      "10946\n",
      "17711\n",
      "28657\n",
      "46368\n",
      "75025\n",
      "121393\n",
      "196418\n",
      "317811\n",
      "514229\n",
      "832040\n",
      "1346269\n"
     ]
    }
   ],
   "source": [
    "\n",
    "# get nth fibonacci number\n",
    "def fib(n):\n",
    "    if n < 2: return n\n",
    "    return fib(n-1) + fib(n-2)\n",
    "\n",
    "# output up to a certain size\n",
    "maxn = 1000000\n",
    "for n in range(2+maxn):\n",
    "    fn = fib(n)\n",
    "    print(fn)\n",
    "    if fn > maxn: break\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 2\n",
    "## write a program to simulate 1000 tosses of a fair coin (use np.random.binomial)\n",
    "## Calculate the mean and standard deviation of that sample"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean: 0.485\n",
      "stddev: 0.4997749493522059\n"
     ]
    }
   ],
   "source": [
    "# simulate 1000 tosses\n",
    "tosses = np.random.binomial(1, 0.5, size=1000)\n",
    "\n",
    "#print(tosses)\n",
    "print(f\"mean: {np.mean(tosses)}\")\n",
    "print(f\"stddev: {np.std(tosses)}\")\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Task 3\n",
    "## Produce a scatterplot of y = 0.5*x+e where x has gaussian (0, 5) and e has gaussian (0, 1) distributions \n",
    "### use numpy.random.normal to generate gaussian distribution"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7f69e06d1940>"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "\n",
    "N = 256\n",
    "x = np.random.normal(0, 5, N)\n",
    "e = np.random.normal(0, 1, N)\n",
    "y = 0.5 * x + e\n",
    "plt.scatter(x, y)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.8.10"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}