spunjani.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": null,
   "metadata": {},
   "outputs": [],
   "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": 11,
   "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"
     ]
    }
   ],
   "source": [
    "n1 = 0\n",
    "n2 = 1\n",
    "count = 0\n",
    "while count < 10: #change to million when done\n",
    "    nth = n1 + n2\n",
    "    print(n1)\n",
    "    n1 = n2\n",
    "    n2 = nth\n",
    "    count += 1"
   ]
  },
  {
   "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:  0.496\n",
      "Standard deviation:  15.677052784244877\n"
     ]
    }
   ],
   "source": [
    "import math\n",
    "\n",
    "x = np.random.binomial(1000, .5, 1)\n",
    "s = sum(x)\n",
    "\n",
    "mean = s/1000\n",
    "\n",
    "variances = [y - mean for y in x]\n",
    "squares = [y*y for y in variances]\n",
    "\n",
    "square_sum = sum(squares)\n",
    "variance = square_sum/(1000-1)\n",
    "\n",
    "std_dev = math.sqrt(variance)\n",
    "\n",
    "print(\"Mean: \", mean)\n",
    "print(\"Standard deviation: \", std_dev)"
   ]
  },
  {
   "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": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "x = np.random.normal(0, 5, 100)\n",
    "e = np.random.normal(0, 1, 100)\n",
    "\n",
    "f = 0.5*x+e\n",
    "\n",
    "plt.scatter(x, f)\n",
    "plt.show()"
   ]
  },
  {
   "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
}