abrock14.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "IPython version:      %6.6s 6.1.0\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",
      "[[ 0.20354485  0.87353642  0.79226415]\n",
      " [ 0.26457656  0.23486214  0.8240387 ]]\n",
      "Add 5 to every element\n",
      "[[ 5.20354485  5.87353642  5.79226415]\n",
      " [ 5.26457656  5.23486214  5.8240387 ]]\n",
      "Get the first row\n",
      "[ 5.20354485  5.87353642  5.79226415]\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": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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aIPsbgIu69+lFwOXj3P4RX/RJnsbg/4CrquqGofHXAK8ELqju5BkHcWuHw+lA2YdcBfxB\ntzzt2Z/H4HzqV5Ls6vLdleQXmf7sVNUTVfWjqvox8Nc8dapgarIfYH/ZDdzQnSr4EvBjBveNmZrc\nsOj7dBXw+8C1Q9NXQvZNwJPLf8+495dJXKCYli8GFzyuBD603/gZDG6pPLPf+Av5yYs8DzO5izwH\nyn7S0PKbgeu75bP5yYs8X5q2132/Obt46mLs1GcH1gwtX8TgHPHU7DOL5H498Kfd8gsYnDbItORe\nan/p3qtf2G9s6rMzOFf/sm75dODObnks+/ph/x8+TV/AbzG4KHIPcHf3dRaDizePDo19fOg5lzC4\niv8g3VXzKcv+KeDebvwfGFygfXKH+2iX/avA7LRl32/OcNFPfXbgb7ts9zC4r9Nw8U98n1kk99HA\n33X7zF3Ay6cp91L7C/BJ4PULPGeqs3fjdzL4hbQD+PVu/lj2df8yVpIad8Sfo5ek1ln0ktQ4i16S\nGmfRS1LjLHpJapxFL0mNs+glqXEWvSQ17v8ApNqW0K2lWVMAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f8a2433ca20>"
      ]
     },
     "metadata": {},
     "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": 8,
   "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"
     ]
    }
   ],
   "source": [
    "end = 1000000\n",
    "n1 = 0\n",
    "n2 = 1\n",
    "\n",
    "for i in range(1, end):\n",
    "    if (n1 > end):\n",
    "        break\n",
    "    print(n1)\n",
    "    n3 = n1 + n2\n",
    "    n1 = n2\n",
    "    n2 = n3"
   ]
  },
  {
   "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": 62,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 519.0\n",
      "Standard deviation: 15.811388300841896\n"
     ]
    }
   ],
   "source": [
    "import numpy as np\n",
    "\n",
    "nflips = 1000\n",
    "ntrials = 1\n",
    "p = 0.50\n",
    "\n",
    "heads = np.random.binomial(nflips, p, ntrials)\n",
    "\n",
    "mean = np.mean(heads)\n",
    "\n",
    "dev = np.sqrt(nflips * p * (1 - p))\n",
    "\n",
    "print(\"Mean: \" + str(mean))\n",
    "print(\"Standard deviation: \" + str(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": 71,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-3.4857440794145518 0.5051479510891475\n",
      "-1.2377240886181284\n"
     ]
    },
    {
     "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": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "x = np.random.normal(0, 5)\n",
    "e = np.random.normal(0, 1)\n",
    "\n",
    "y = 0.5 * x + e\n",
    "\n",
    "plt.scatter(x, y)\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
}