Homework 7 Answers.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Homework 7: Demonstrate Central Tendency and the Normal Distribution\n",
    "\n",
    "Useful Packages:\n",
    "  - numpy\n",
    "    - numpy.random\n",
    "  - ipywidgets\n",
    "    - ipywidgets.interact\n",
    "  - matplotlib"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1) Write a function that returns N random values taken from a uniform distribution of values between 0 and 1.\n",
    "```python\n",
    "def uniform_gen(N):\n",
    "   \"\"\"returns N random values\"\"\"\n",
    "\n",
    "uniform_gen(N=5)\n",
    ">> [.4, .9, .1, .2, .4]\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from numpy import random\n",
    "import matplotlib.pyplot as plt\n",
    "import ipywidgets as widg\n",
    "from ipywidgets import interact\n",
    "\n",
    "%matplotlib inline"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def uniform_gen(N):\n",
    "    return random.uniform(low=0.0, high=1.0, size=N)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1b) Demonstrate the function's working by plotting its output in a histogram."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXUAAAEACAYAAABMEua6AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nlrokNeT/AVbnsGH1ti+YAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3f9861748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = plt.hist(uniform_gen(300))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1c) Make the plot interactive, allowing a user to move a slider widget to change the value of N"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEACAYAAACwB81wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3f95ed3c8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def uniform_plot(N):\n",
    "    plt.hist(uniform_gen(N), bins=7)\n",
    "    \n",
    "interact(uniform_plot, N=300)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Write a function that takes an array of data and returns M random values from that array.\n",
    "```python\n",
    "def random_choice(data, M):\n",
    "    \"\"\"returns M random values from 'data'\"\"\"\n",
    "    \n",
    "random_choice(data=[.4, .9, .1, .2, .4], M=3)\n",
    ">> [.9, .1, .2]\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def random_choice(data, M):\n",
    "    return random.choice(data, M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 3) Write a function that calls a given function P times and returns the mean of the function's output.\n",
    "\n",
    "```python\n",
    "def function_means(fun, P, *args, **kwargs):\n",
    "   \"\"\"calls fun(*args, **kwargs) P times, returning a list of means of fun's output.\"\"\"\n",
    "   \n",
    "function_means(fun=random_choice, P=7, data=[.4, .9, .1, .2, .4], M=3)\n",
    ">> [.43, .32, .71, .66, .54, .33, .59]\n",
    "```"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def function_means(fun, P, *args, **kwargs):\n",
    "    return [np.mean(fun(*args, **kwargs)) for el in range(P)]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4) Write the Mega-Function, which takes P means from random-choice samples of M length from N uniformly-generated random values.\n",
    "\n",
    "```python\n",
    "def means_from_uniform_data(N, M, P):\n",
    "   \"\"\"\n",
    "   returns a list of means of length P, obtained by getting \n",
    "   random subsets of length M from a randomly-generated sample of length N\n",
    "   \"\"\"\n",
    "   \n",
    "means_from_uniform_data(N=100, M=20, P=5)\n",
    ">> [.45, .72, .55, .46, .69]\n",
    "```\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def means_from_uniform_data(N, M, P):\n",
    "    return function_means(random_choice, P=P, data=uniform_gen(N), M=M)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 4b) Plot a histogram of results from mean_from_uniform_data() when N=200, M=20, and P=2000.\n",
    "Note: The resulting histogram should have a gaussian distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(array([   5.,   32.,  104.,  276.,  416.,  565.,  394.,  163.,   37.,    8.]),\n",
       " array([ 0.26590526,  0.30938469,  0.35286412,  0.39634355,  0.43982298,\n",
       "         0.48330241,  0.52678184,  0.57026127,  0.6137407 ,  0.65722013,\n",
       "         0.70069956]),\n",
       " <a list of 10 Patch objects>)"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXwAAAEACAYAAACwB81wAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nSWqEgS9JjTDwJakR/weJCVhvXiMUbwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3f9828550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.hist(means_from_uniform_data(N=500, M=20, P=2000))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 5) Make the Plot from 4b interactive, allowing the user to change N, M, and P"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXkAAAEACAYAAABWLgY0AAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7ff3f94bd080>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def plot_means(N=500, M=20, P=2000):\n",
    "    plt.hist(means_from_uniform_data(N=N, M=M, P=P))\n",
    "    \n",
    "interact(plot_means, \n",
    "         N=widg.IntSlider(value=10, min=7, max=1000),\n",
    "         M=widg.IntSlider(value=10, min=7, max=1000),\n",
    "         P=widg.IntSlider(value=10, min=7, max=1000),\n",
    "        )    "
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.4.3"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}