jclar168.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",
      "[[0.93690312 0.56727454 0.42590333]\n",
      " [0.68248552 0.48403269 0.27349487]]\n",
      "Add 5 to every element\n",
      "[[5.93690312 5.56727454 5.42590333]\n",
      " [5.68248552 5.48403269 5.27349487]]\n",
      "Get the first row\n",
      "[5.93690312 5.56727454 5.42590333]\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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l64uAm7vNbgD+rC/ropzTJV/u/ZKMA68Atk1bdTq939ww81sf7K8Uhm56ziQfS/Iw8Gbgw91mSypnkvXA7qq6fdpmSypnN/Tu7s/vi5Mc3o2NPCc8KeuLgFcn2Zbka0l+t9ts5Fn38bP0auDRqnqgu73Ucr4P+Hj3s/QJ4Jxus5HnhCdlvZsn3k/rz3niRZ2LlvWgKfckzwS+ALyv/2o4ybnAXuCyUWXrN1POqjq3qtbQy/juUeZ7XH9OeufvQzzxi2fJmOF8Xgi8AHg5sIfeNMKSMEPWZcAR9KYK/gq4srs6Hql9/SwBp/HEVfvIzZDzHcBZ3c/SWcBFo8zXb4aspwPvTLKd3nTNLxY700FR7kmeSu/EXVZVV/eNvxV4A/Dm6ia0GOFbH+wrZ5/LeOLPs6WU8wX05v9uT7Kzy3Jrkt9cYjmpqker6pdV9SvgszzxJ+1I3/JiH9/7XcDV3XTBN4Bf0XsjqSV1TrvxZcCfAlf0bb7Ucm4AHl/+F5bw976q7quq11XVK+n9wvzOomddiIn8YX7Qe5DkUuDvp42vA+4BxqaNv4Rff8DiQRbnQaB95Tyqb/k9wFXd8kn8+oNA3xjl+Zy2zU6eeEB1SeUEVvYtn0Vv/nJk3/dZsr4d+Otu+UX0/hzPUruPduvWAV+bNrakctKbz35Nt3w8sH2U99FZsj7+4PlTuvWnL/Y5XZQTMODJ+wN6D6TcAdzWfZxI74GIh/vGPtO3z7n0flPeT/fo+ghzfgG4qxv/Er0HWR+/U3y6y3knMDHKnNO22ckT5b6kcgL/1OW4g977FfWX/aJ/32fJeijwz933/1bgtUvxPtqtuwR4+wz7LJmc3fh2euW4DXjlKO+js2Q9k94zZ74NbKZ7N4DFPKe+/YAkNeigmHOXJM2N5S5JDbLcJalBlrskNchyl6QGWe6S1CDLXZIa9P85K7KYy4WvQQAAAABJRU5ErkJggg==\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": 6,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "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": [
    "current = 1\n",
    "previous = np.array([0,1])\n",
    "next_index = 0\n",
    "\n",
    "while (current < 1000000):\n",
    "    if (current < 1000000):\n",
    "        print(current)\n",
    "    current = sum(previous)\n",
    "    previous[next_index] = current\n",
    "    next_index = 1-next_index"
   ]
  },
  {
   "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": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Mean: 499.1\n",
      "Stdev: 16.175598906995685\n"
     ]
    }
   ],
   "source": [
    "result = np.random.binomial(1000,0.5, 100)\n",
    "print('Mean:',np.mean(result))\n",
    "print('Stdev:',np.std(result))"
   ]
  },
  {
   "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": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.collections.PathCollection at 0x7fcfc44a3610>"
      ]
     },
     "execution_count": 20,
     "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": [
    "e = np.random.normal(0, 1, 100)\n",
    "x = np.random.normal(0, 5, 100)\n",
    "y = 0.5*x+e\n",
    "import matplotlib.pyplot as plt\n",
    "plt.scatter(x, y)"
   ]
  },
  {
   "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
}