{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "## CS 237 Homework 01 -- Data Visualization in Python\n", "\n", "### Due Thursday February 4th at Midnight (1 minute after 11:59pm) in Gradescope (with grace period of 6 hours)\n", "### Homeworks may be submitted up to 24 hours late with a 10% penalty (same grace period)\n", "\n", "In this first homework, you will become familiar with various methods of displaying the results of probability experiments graphically in Python using Jupyter notebooks and Matplotlib. This will be a fundamental way of understanding the results of experiments throughout the course. \n", "\n", "Please read through the entire notebook, following the instuctions to try various features; among the exposition of various features of Python there\n", "are five problems which will be graded. The homework is worth 60 points (same as a normal homework), so each problem is worth 12 points. \n", "\n", "To submit, be sure to click on Run All and verify that everything works as you intended, and then upload the file to Gradescope. " ] }, { "cell_type": "code", "execution_count": 66, "metadata": {}, "outputs": [], "source": [ "# Here are some imports which will be used in the code in the rest of the lab \n", "\n", "# Imports used for the code in CS 237\n", "\n", "import numpy as np # arrays and functions which operate on array\n", "import matplotlib.pyplot as plt # normal plotting\n", "\n", "\n", "from numpy.random import seed, randint, random\n", "from collections import Counter\n", "\n", "# NOTE: You may not use any other libraries than those listed here without explicit permission." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Getting Started with Data Visualization in Jupyter Notebooks\n", "\n", "In this homework, we will begin our study of probability in computing by exploring various ways of displaying data, especially data created by random processes. We shall use a library numpy.random (imported in the previous code cell) to generate random numbers and display the results.\n", "\n", " If you need a refresher on Python, please download and work through the PythonForCS237.ipynb notebook from the class web page in addition to this homework. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plotting Individual Data Points\n", "\n", "The scatter(...) function is used to plot points from a list of x values and the associated y values. " ] }, { "cell_type": "code", "execution_count": 67, "metadata": { "scrolled": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "Here is the list of points: [(1, 2), (2, 4), (3, 6), (4, 8)]\n", "They must be input to the function as separate lists, which must be the same length:\n", "\tX = [1, 2, 3, 4]\n", "\tY = [2, 4, 6, 8] \n", "\n" ] }, { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# To plot the points (1,2), (2,4), (3,6), (4,8) we would list the x values and the corresponding y values:\n", "X = [1,2,3,4]\n", "Y = [2,4,6,8]\n", "\n", "print(\"\\nHere is the list of points:\",list(zip(X,Y)))\n", "print(\"They must be input to the function as separate lists, which must be the same length:\")\n", "print(\"\\tX =\",X)\n", "print(\"\\tY =\",Y,\"\\n\")\n", "plt.scatter(X,Y)\n", "plt.title('Graphing Points with scatter (X,Y)')\n", "plt.xlabel(\"The X Values\")\n", "plt.ylabel(\"The Y Values\")\n", "plt.show()\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### TODO (no credit, but don't skip this)\n", "\n", "Extend the previous example so that it plots the points `(5,10)` and `(6,12)` as well. Just change the code in the previous cell. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## List Comprehensions\n", "\n", "A list comprehension is a great way to create lists with a minimum of fuss and bugs. \n", "The basic idea is that instead of creating a list by specifying every step, say like this:" ] }, { "cell_type": "code", "execution_count": 68, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]\n" ] } ], "source": [ "# Create a list of the first 10 squares\n", "\n", "L = [0] * 10 # create a list of 10 zeros\n", "for k in range(len(L)):\n", " L[k] = (k+1)**2\n", " \n", "print(L)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "you can do it all in one line:" ] }, { "cell_type": "code", "execution_count": 69, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[1, 4, 9, 16, 25, 36, 49, 64, 81, 100]\n" ] } ], "source": [ "L1 = [ (k+1)**2 for k in range(len(L)) ]\n", "print(L1)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The idea is to collect together all instances of the expression at the beginning, for all values of k produces\n", "by the (implicit) `for` loop. We will use list comprehensions throughout the course, and you should definitely become good friends with them, they will simplify your Python code!\n", "\n", "In the next two examples, we show more complicated kinds of list comprehensions, the first using a condition to filter the list, and in the second, using *two* for loops:" ] }, { "cell_type": "code", "execution_count": 70, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[0, 4, 16]\n" ] } ], "source": [ "D = [0,1,2,3,4]\n", "\n", "# Just print out the squares of the even numbers\n", "\n", "print( [ d**2 for d in D if d % 2 == 0 ] )" ] }, { "cell_type": "code", "execution_count": 71, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "['AA', 'AB', 'AC', 'AD', 'AE', 'BA', 'BB', 'BC', 'BD', 'BE', 'CA', 'CB', 'CC', 'CD', 'CE', 'DA', 'DB', 'DC', 'DD', 'DE', 'EA', 'EB', 'EC', 'ED', 'EE']\n" ] } ], "source": [ "L = ['A','B','C','D','E']\n", "\n", "# Enumerate all two letter sequence of the letters in L\n", "\n", "print( [ l1 + l2 for l1 in L for l2 in L ] )" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Plotting Lines and Curves\n", "\n", "If you call plot(...) instead of scatter(...) you will display a curve created by connecting the points with straight lines. Essentially you can only plot straight lines between points, but if the points are close together, you will not notice, and it will look like a smooth curve. \n", "\n", "Here we will use our first function from the `numpy` library, which allows you to create a linearly-spaced sequence of floating-point numbers between two (inclusive) bounds. " ] }, { "cell_type": "code", "execution_count": 72, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# To plot a curve through the points (1,2), (2,3), (3,7), (4,8) we would use: \n", "plt.plot([1,2,3,4], [2,3,7,8])\n", "plt.title('A Sequence of Straight Lines')\n", "plt.xlabel(\"The X Values\")\n", "plt.ylabel(\"The Y Values\")\n", "plt.show()\n", "\n", "X = np.linspace(0,2*np.pi,100) # returns a list of 100 equally-spaced values in the range [0..2*pi]\n", "Y = [ np.sin(x) for x in X ] \n", "plt.plot(X,Y)\n", "plt.title('A Smooth-Looking Curve')\n", "plt.xlabel(\"The X Values\")\n", "plt.ylabel(\"The Y Values\")\n", "plt.show()\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "If you want to do both, you can simply call both functions before you call show(). " ] }, { "cell_type": "code", "execution_count": 73, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.plot([1,2,3,4], [2,3,7,8])\n", "plt.scatter([1,2,3,4], [2,3,7,8])\n", "plt.title('A Curve Through Some Points, Showing the Points')\n", "plt.xlabel(\"The X Values\")\n", "plt.ylabel(\"The Y Values\")\n", "plt.show()" ] }, { "attachments": { "Screen%20Shot%202021-01-29%20at%209.37.05%20AM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "### TODO (no credit, but don't skip this)\n", "\n", "If you want to draw a single line from $(x_1,y_1)$ to $(x_2,y_2)$ you can plot $[x_1,x_2]$ and $[y_1,y_2].$\n", "\n", "Change the code for drawing the sin curve above so that it has an X-axis, producing the following:\n", "\n", "![Screen%20Shot%202021-01-29%20at%209.37.05%20AM.png](attachment:Screen%20Shot%202021-01-29%20at%209.37.05%20AM.png)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "For further details on drawing plots, particularly on color and format, see the `PythonForCS237.ipynb` document on the class web page. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Using the Numpy Random Library\n", "\n", "We have imported a number of functions from the Numpy Random library, which are explained in detail in the `NumpyTutorial.ipynb` notebook on the class web page. For more information, look \n", " here. " ] }, { "cell_type": "code", "execution_count": 74, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0.5488135039273248" ] }, "execution_count": 74, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Run this cell several times and and see what happens\n", "\n", "random()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This function generates random floats in a particular range -- what is that range?" ] }, { "cell_type": "code", "execution_count": 75, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.7151893663724195,\n", " 0.6027633760716439,\n", " 0.5448831829968969,\n", " 0.4236547993389047,\n", " 0.6458941130666561,\n", " 0.4375872112626925,\n", " 0.8917730007820798,\n", " 0.9636627605010293,\n", " 0.3834415188257777,\n", " 0.7917250380826646]" ] }, "execution_count": 75, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Run this cell several times and and see what happens\n", "# List comprehensions are your best friend, learn how to use them!!!\n", "\n", "size = 10\n", "rands = [ random() for k in range(size) ]\n", "rands" ] }, { "cell_type": "code", "execution_count": 76, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.52889492, 0.56804456, 0.92559664, 0.07103606, 0.0871293 ])" ] }, "execution_count": 76, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Run this cell several times and and see what happens!\n", "# This produces a Numpy 1D vector, which is\n", "# another way to store a sequence.\n", "\n", "size = 5\n", "random(size)" ] }, { "cell_type": "code", "execution_count": 77, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "[0.02021839744032572,\n", " 0.832619845547938,\n", " 0.7781567509498505,\n", " 0.8700121482468192,\n", " 0.978618342232764]" ] }, "execution_count": 77, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# In most cases, arrays are interchangeable with lists, but if you need a Python \n", "# list, just do this:\n", "\n", "list(random(size))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In order to make grading easier, we will \"seed\" the random number generation so that it always produces the same pseudo-random sequence. However, you should generally try running your code several times without the seed, trying it on various random sequences. \n", "\n", "Note: Just be sure to include the seed before running your program to submit, so that the graders can see your correct results. \n" ] }, { "cell_type": "code", "execution_count": 78, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([0.5488135 , 0.71518937, 0.60276338, 0.54488318, 0.4236548 ])" ] }, "execution_count": 78, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Run this cell several times, and see what happens.\n", "# Then comment out the line and run it again several times. You should see that it does not change if the seed \n", "# is specified. It is usual to seed the random number generator with 0. \n", "\n", "seed(0) # to comment out this line, put at # at the beginning: #seed(0)\n", "random(5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### TODO (no credit, but don't skip this)\n", "\n", "Suppose you want 10 random floating-point numbers in the range $[0 .. 100]$ instead of $[0..1]$?\n", "\n", "In the next cell, write the code that would produce a list of 10 such numbers. \n" ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [] }, { "attachments": { "image.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "Ok, now it is your turn!\n", "\n", "\n", "\n", "# Problem 1 (Plotting Points)\n", "\n", "## Part A\n", "\n", "One of our standard examples in lecture will be a \"spinner\" which can be set in motion to\n", "randomly chose a real number in the half-open interval [0..1): \n", "\n", "![image.png](attachment:image.png)\n", "\n", "\n", "We will simulate this using the Python function random() from the Numpy.random library we imported above.\n", "\n", "\n", "Use `numpy`'s `random()` function to build a list `x_vals` with the following properties: \n", " - The `x_vals` list should have length `num_trials`\n", " - Each value in `x_vals` should be a random float in the range $[0..1)$\n", " \n", "Now plot the points $(x_i,0)$ along the X-axis in the diagram below\n" ] }, { "cell_type": "code", "execution_count": 79, "metadata": {}, "outputs": [ { "data": { "image/png": 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BJHlSknXAC4D3JbmyX/0xwGVJvglcBJw2dFUSSZIkabvTYrgIVXUecN7QvJMHnl9KN4xkeL0vA/+1RR8kSZKkhcI7PkqSJEmNGbIlSZKkxgzZkiRJUmOGbEmSJKkxQ7YkSZLUmCFbkiRJasyQLUmSJDVmyJYkSZIaM2RLkiRJjRmyJUmSpMYM2ZIkSVJjhmxJkiSpMUO2JEmS1JghW5IkSWrMkC1JkiQ1ZsiWJEmSGjNkS5IkSY0ZsiVJkqTGDNmSJElSY01CdpIjk1ydZG2Sk0Ysf1qSryfZmOSYoWUrk1zTP1a26I8kSZI0nyYO2Ul2AN4NPBs4EHhxkgOHml0PHAd8bGjd3YBTgCcDhwCnJNl10j5JkiRJ86nFkexDgLVVdW1V/RQ4Czh6sEFVXVdVVwCbhtZ9FnBBVW2oqtuAC4AjG/RJkiRJmjdLGmxjL+CGgel1dEemt3bdvUY1TLIKWAWwbNkypqam5t5TLWqbNm2yLrQF60KjWBcaxbpQSy1CdkbMq9brVtVqYDXAihUraunSpWPuQvcXU1NTWBcaZl1oFOtCo1gXaqnFcJF1wLKB6b2B9dtgXUmSJGlBahGyLwWWJ9kvyY7AscCaMdc9Hzgiya79CY9H9PMkSZKk7dbEIbuqNgKvoQvH/wJ8oqquTHJqkqMAkjwpyTrgBcD7klzZr7sBeAtdUL8UOLWfJ0mSJG23WozJpqrOA84bmnfywPNL6YaCjFr3dOD0Fv2QJEmSFgLv+ChJkiQ1ZsiWJEmSGjNkS5IkSY0ZsiVJkqTGDNmSJElSY4ZsSZIkqTFDtiRJktSYIVuSJElqzJAtSZIkNWbIliRJkhozZEuSJEmNGbIlSZKkxgzZkiRJUmOGbEmSJKkxQ7YkSZLUmCFbkiRJasyQLUmSJDVmyJYkSZIaaxKykxyZ5Ooka5OcNGL5TknO7pdfkmTffv6+Se5Kcnn/eG+L/kiSJEnzacmkG0iyA/Bu4HBgHXBpkjVVddVAs+OB26rq0UmOBd4OvKhf9p2qOmjSfkiSJEkLRYsj2YcAa6vq2qr6KXAWcPRQm6OBM/rnnwQOTZIG+5YkSZIWnImPZAN7ATcMTK8Dnjxdm6ramOQOYPd+2X5JvgH8EHhjVX1x1E6SrAJWASxbtoypqakGXddismnTJutCW7AuNIp1oVGsC7XUImSPOiJdY7a5EXhUVd2a5InAp5I8tqp+uEXjqtXAaoAVK1bU0qVLJ+y2FpupqSmsCw2zLjSKdaFRrAu11GK4yDpg2cD03sD66dokWQI8FNhQVXdX1a0AVfXPwHeAAxr0SZIkSZo3LUL2pcDyJPsl2RE4Flgz1GYNsLJ/fgzw+aqqJA/rT5wkyf7AcuDaBn2SJEmS5s3Ew0X6MdavAc4HdgBOr6ork5wKXFZVa4APAGcmWQtsoAviAE8DTk2yEbgHeFVVbZi0T5IkSdJ8ajEmm6o6DzhvaN7JA89/ArxgxHp/B/xdiz5IkiRJC4V3fJQkSZIaM2RLkiRJjRmyJUmSpMYM2ZIkSVJjhmxJkiSpMUO2JEmS1JghW5IkSWrMkC1JkiQ1ZsiWJEmSGjNkS5IkSY0ZsiVJkqTGDNmSJElSY4ZsSZIkqTFDtiRJktSYIVuSJElqzJAtSZIkNWbIliRJkhozZEuSJEmNNQnZSY5McnWStUlOGrF8pyRn98svSbLvwLLX9/OvTvKsFv2RJEmS5tPEITvJDsC7gWcDBwIvTnLgULPjgduq6tHAO4G39+seCBwLPBY4EnhPvz1JkiRpu7WkwTYOAdZW1bUASc4CjgauGmhzNPDm/vkngXclST//rKq6G/hukrX99r4y0w6vu/XHvOh9MzbR/dCmTffwgAf4HU33Zl1oFOtCo1gXaqlFyN4LuGFgeh3w5OnaVNXGJHcAu/fzvzq07l6jdpJkFbAKYOme+7Np0z0Nuq7FpArrQluwLjSKdaFRrAu11CJkZ8S8GrPNOOt2M6tWA6sBVqxYUef8zq/NpY+6H5iammLp0qXz3Q0tMNaFRrEuNIp1oWF59dav2+LEx3XAsoHpvYH107VJsgR4KLBhzHUlSZKk7UqLkH0psDzJfkl2pDuRcc1QmzXAyv75McDnq6r6+cf2Vx/ZD1gOfK1BnyRJkqR5M/FwkX6M9WuA84EdgNOr6sokpwKXVdUa4APAmf2JjRvogjh9u0/QnSS5EfgfVeVgKEmSJG3XWozJpqrOA84bmnfywPOfAC+YZt23AW9r0Q9JkiRpIfCOj5IkSVJjhmxJkiSpMUO2JEmS1JghW5IkSWrMkC1JkiQ1ZsiWJEmSGjNkS5IkSY0ZsiVJkqTGDNmSJElSY4ZsSZIkqTFDtiRJktSYIVuSJElqzJAtSZIkNWbIliRJkhozZEuSJEmNGbIlSZKkxgzZkiRJUmOGbEmSJKmxiUJ2kt2SXJDkmv7nrtO0W9m3uSbJyoH5Fye5Osnl/ePhk/RHkiRJWggmPZJ9EnBhVS0HLuyn7yXJbsApwJOBQ4BThsL4S6rqoP5x84T9kSRJkubdpCH7aOCM/vkZwPNHtHkWcEFVbaiq24ALgCMn3K8kSZK0YC2ZcP1HVNWNAFV14zTDPfYCbhiYXtfP2+yDSe4B/g54a1XVqB0lWQWsAli2bBlTU1MTdl2LzaZNm6wLbcG60CjWhUaxLtTSrCE7yeeAR45Y9IYx95ER8zYH6ZdU1feTPJguZL8M+PCojVTVamA1wIoVK2rp0qVj7l73F1NTU1gXGmZdaBTrQqNYF2pp1pBdVYdNtyzJTUn27I9i7wmMGlO9DnjGwPTewMX9tr/f/7wzycfoxmyPDNmSJEnS9mLSMdlrgM1XC1kJnDuizfnAEUl27U94PAI4P8mSJHsAJHkg8Fzg2xP2R5IkSZp3k4bs04DDk1wDHN5Pk+TgJO8HqKoNwFuAS/vHqf28nejC9hXA5cD3gb+dsD+SJEnSvJvoxMequhU4dMT8y4BXDkyfDpw+1GYKeOIk+5ckSZIWIu/4KEmSJDVmyJYkSZIaM2RLkiRJjRmyJUmSpMYM2ZIkSVJjhmxJkiSpMUO2JEmS1JghW5IkSWrMkC1JkiQ1ZsiWJEmSGjNkS5IkSY0ZsiVJkqTGDNmSJElSY4ZsSZIkqTFDtiRJktSYIVuSJElqzJAtSZIkNWbIliRJkhqbKGQn2S3JBUmu6X/uOk27zya5Pcmnh+bvl+SSfv2zk+w4SX8kSZKkhWDSI9knARdW1XLgwn56lHcALxsx/+3AO/v1bwOOn7A/kiRJ0rybNGQfDZzRPz8DeP6oRlV1IXDn4LwkAX4D+ORs60uSJEnbkyUTrv+IqroRoKpuTPLwOay7O3B7VW3sp9cBe03XOMkqYBXAsmXLmJqa2soua7HatGmTdaEtWBcaxbrQKNaFWpo1ZCf5HPDIEYveMOG+M2JeTde4qlYDqwFWrFhRS5cunXD3WmympqawLjTMutAo1oVGsS7U0qwhu6oOm25ZkpuS7Nkfxd4TuHkO+74F2CXJkv5o9t7A+jmsL0mSJC1Ik47JXgOs7J+vBM4dd8WqKuAi4JitWV+SJElaqCYN2acBhye5Bji8nybJwUnev7lRki8C5wCHJlmX5Fn9otcBJyRZSzdG+wMT9keSJEmadxOd+FhVtwKHjph/GfDKgelfn2b9a4FDJumDJEmStNB4x0dJkiSpMUO2JEmS1JghW5IkSWrMkC1JkiQ1ZsiWJEmSGjNkS5IkSY0ZsiVJkqTGDNmSJElSY4ZsSZIkqTFDtiRJktSYIVuSJElqzJAtSZIkNWbIliRJkhozZEuSJEmNGbIlSZKkxgzZkiRJUmOGbEmSJKkxQ7YkSZLU2EQhO8luSS5Ick3/c9dp2n02ye1JPj00/0NJvpvk8v5x0CT9kSRJkhaCSY9knwRcWFXLgQv76VHeAbxsmmV/UFUH9Y/LJ+yPJEmSNO8mDdlHA2f0z88Anj+qUVVdCNw54b4kSZKk7cKkIfsRVXUjQP/z4VuxjbcluSLJO5PsNGF/JEmSpHm3ZLYGST4HPHLEojc02P/rgR8AOwKrgdcBp07Tj1XAKoBly5YxNTXVYPdaTDZt2mRdaAvWhUaxLjSKdaGWZg3ZVXXYdMuS3JRkz6q6McmewM1z2fnmo+DA3Uk+CPz+DG1X0wVxVqxYUUuXLp3LrnQ/MDU1hXWhYdaFRrEuNIp1oZYmHS6yBljZP18JnDuXlftgTpLQjef+9oT9kSRJkubdpCH7NODwJNcAh/fTJDk4yfs3N0ryReAc4NAk65I8q1/00STfAr4F7AG8dcL+SJIkSfNu1uEiM6mqW4FDR8y/DHjlwPSvT7P+b0yyf0mSJGkh8o6PkiRJUmOGbEmSJKkxQ7YkSZLUmCFbkiRJasyQLUmSJDVmyJYkSZIaM2RLkiRJjRmyJUmSpMYM2ZIkSVJjhmxJkiSpMUO2JEmS1JghW5IkSWrMkC1JkiQ1ZsiWJEmSGjNkS5IkSY0ZsiVJkqTGDNmSJElSY4ZsSZIkqTFDtiRJktTYRCE7yW5JLkhyTf9z1xFtDkrylSRXJrkiyYsGlu2X5JJ+/bOT7DhJfyRJkqSFYNIj2ScBF1bVcuDCfnrYj4GXV9VjgSOBv0yyS7/s7cA7+/VvA46fsD+SJEnSvJs0ZB8NnNE/PwN4/nCDqvq3qrqmf74euBl4WJIAvwF8cqb1JUmSpO3NkgnXf0RV3QhQVTcmefhMjZMcAuwIfAfYHbi9qjb2i9cBe82w7ipgVT95d5JvT9h3LT57ALfMdye04FgXGsW60CjWhYb90tauOGvITvI54JEjFr1hLjtKsidwJrCyqjb1R7KH1XTrV9VqYHW/rcuq6uC57F+Ln3WhUawLjWJdaBTrQsOSXLa1684asqvqsBl2fFOSPfuj2HvSDQUZ1e4hwGeAN1bVV/vZtwC7JFnSH83eG1g/51cgSZIkLTCTjsleA6zsn68Ezh1u0F8x5O+BD1fVOZvnV1UBFwHHzLS+JEmStL2ZNGSfBhye5Brg8H6aJAcneX/f5oXA04DjklzePw7ql70OOCHJWrox2h8Yc7+rJ+y3FifrQqNYFxrFutAo1oWGbXVNpDugLEmSJKkV7/goSZIkNWbIliRJkhpb0CE7yZFJrk6yNskWd5NMslN/O/a1/e3Z9932vdS2NEZNnJDkqiRXJLkwyT7z0U9tW7PVxUC7Y5JUEi/RdT8wTl0keWH/O+PKJB/b1n3UtjfG/yOPSnJRkm/0/5f85nz0U9tWktOT3DzdfVjS+au+bq5IsmK2bS7YkJ1kB+DdwLOBA4EXJzlwqNnxwG1V9WjgnXS3adciNWZNfAM4uKp+me5uon+2bXupbW3MuiDJg4HfAy7Ztj3UfBinLpIsB14PPLWqHgv8z23eUW1TY/6+eCPwiap6AnAs8J5t20vNkw8BR86w/NnA8v6xCvib2Ta4YEM2cAiwtqquraqfAmfR3cZ90OBt3T8JHDrNTW60OMxaE1V1UVX9uJ/8Kt3117W4jfO7AuAtdF+6frItO6d5M05d/Dbw7qq6DaCqRt7rQYvKOHVRwEP65w/Fe3jcL1TVF4ANMzQ5mu5y1NXf82WX/h4x01rIIXsv4IaB6VG3Xf95m/6GNnfQXQpQi9M4NTHoeOAf7tMeaSGYtS6SPAFYVlWf3pYd07wa5/fFAcABSf4pyVeTzHQUS4vDOHXxZuClSdYB5wG/u226pgVurhlk9js+zqNxbrs+p1uza7s39ued5KXAwcDT79MeaSGYsS6SPIBuONlx26pDWhDG+X2xhO5Pv8+g+6vXF5M8rqpuv4/7pvkzTl28GPhQVf15kl8FzuzrYtN93z0tYHPOnAv5SPY6YNnA9Kjbrv+8TZIldH/WmelQv7Zv49QESQ4D3gAcVVV3b6O+af7MVhcPBh4HXJzkOuBXgDWe/Ljojft/yLlV9bOq+i5wNV3o1uI1Tl0cD3wCoKq+AjwI2GOb9E4L2VgZZNBCDtmXAsuT7Nffmv1Yutu4Dxq8rfsxwOfLu+ssZrPWRD8s4H10AdvxlfcPM9ZFVd1RVXtU1b5VtS/dWP2jquqy+emutpFx/g/5FPBMgCR70A0fuXab9lLb2jh1cT1wKECSx9CF7H/fpr3UQg9xhyMAAADTSURBVLQGeHl/lZFfAe6oqhtnWmHBDhepqo1JXgOcD+wAnF5VVyY5FbisqtbQ3Yb9zP627Bvo/rFokRqzJt4B7Ayc058De31VHTVvndZ9bsy60P3MmHVxPnBEkquAe4A/qKpb56/Xuq+NWRcnAn+b5LV0wwGO8wDe4pfk43RDx/box+OfAjwQoKreSzc+/zeBtcCPgVfMuk3rRpIkSWprIQ8XkSRJkrZLhmxJkiSpMUO2JEmS1JghW5IkSWrMkC1JkiQ1ZsiWJEmSGjNkS5IkSY39f4SbFK33ANpdAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# TO DO: Complete the lines of code indicated above. Then comment out the seed(0) \n", "# statement and run this cell several times to see the distribution of points;\n", "# put the seed command back in before you submit!\n", "\n", "def random_line_plot(num_trials):\n", " x_vals = [ ] # <--- Your code here\n", " y_vals = [ ] # <--- Your code here\n", " plt.figure(figsize=(12, 4))\n", " plt.title('Graph of Uniform Distribution of '+str(num_trials)+' points in 1D.',fontsize=12)\n", " plt.grid(color='0.95')\n", " plt.ylim(-0.2, 0.2)\n", " plt.xlim(-0.0,1.0)\n", " plt.plot([0,1.0],[0,0])\n", " plt.scatter(x_vals, y_vals, marker=\"x\",color=\"r\")\n", " plt.show()\n", "\n", "\n", "seed(0) # Try this with and without the seed, to see the effect; include the seed 0 when submitting!\n", "random_line_plot(50)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Part B\n", "\n", "Now we will simulate the experiment of throwing a dart at a unit square, which will produce a scatter plot of random points in a 2D grid. This should look familiar: we examined such a data visualization in the last lecture!\n", "\n", "Use `numpy`'s `random` function to build a list of x and y values with the following properties: \n", " - `x_vals` and `y_vals` should both have length `num_trials`\n", " - Each value in x and y should be in the range $[0..1)$. \n", " \n", "HINT: use the same code to build `x_vals` and `y_vals`. \n", " " ] }, { "cell_type": "code", "execution_count": 80, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# TO DO: Complete the following function stub which will produce a scatter plot of \n", "# random points in a unit square. \n", "\n", "def random_plane_plot(num_trials):\n", " x_vals = [ ] # Your code here\n", " y_vals = [ ] # Your code here\n", " plt.figure(num=None, figsize=(10, 10))\n", " plt.title('Graph of Uniform Distribution of '+str(num_trials)+' points in 2D.',fontsize=12)\n", " plt.grid(color='0.95')\n", " plt.ylim(0, 1)\n", " plt.xlim(0,1)\n", " plt.scatter(x_vals, y_vals,marker=\"o\",color=\"r\")\n", " plt.show()\n", "\n", " \n", "# Comment out the next line and run this cell several times to see the distribution of points;\n", "# put the seed command back in before you submit!\n", "\n", "# Then try generating 300, and then 3000 points! Submit your solution with 3000 points. \n", "\n", "seed(0)\n", "random_plane_plot(30)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Bar Charts\n", "\n", "If we do the exact same thing as we did with a simple plot, but use the function bar(...) we get a bar chart:" ] }, { "cell_type": "code", "execution_count": 81, "metadata": {}, "outputs": [ { "data": { "image/png": "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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# To plot the points (1,2), (2,4), (3,6), (4,8) we would list the x values and the corresponding y values:\n", "plt.figure(figsize=(8, 6))\n", "plt.bar([1,2,3,4], [2,4,6,8])\n", "plt.title('A Bar Chart')\n", "plt.xlabel(\"Number\")\n", "plt.ylabel(\"Frequency\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "If the Y axis is probabilities (in the range 0 .. 1), we get a distribution of the probabilities among the outcomes of an experiment:" ] }, { "cell_type": "code", "execution_count": 82, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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fYFlVXV1VdwFnA4cMTlBV11TVZcC942dO8gTgN4EvdFijJEm91GXA7wqsGOhf2Q6bVJL7Ae8G/qKDuiRJ6r0uAz4TDKsh530FsLiqVqxroiTHJFmSZMmqVaumXKAkSX01s8NlrwTmDPTPBq4fct4nAU9J8grgQcDWSe6oqjUu1KuqU4BTABYsWDDszoMkSb3XZcBfAuyZZHfgOmAh8KJhZqyqI8a6kxwFLBgf7tLmZJfZc7nxunU2SAlgxlYkEzX+jc7Ou87hhpXLR12GNGWdBXxVrU5yLHABMAM4raqWJjkRWFJVi5LsA3wa2BF4dpK3VdVeXdUkjcqN161gt+POH3UZa7j2pINGXcJ93XO320naSLo8gqeqFgOLxw07YaD7Epqm+3Ut43Tg9A7KkySpt7yTnSRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST3UacAnOSDJVUmWJTl+gvH7Jbk0yeokhw4M3zvJ15MsTXJZkhd2WackSX3TWcAnmQGcDBwIzAcOTzJ/3GTLgaOAj44b/gvgJVW1F3AA8L4kO3RVqyRJfTOzw2XvCyyrqqsBkpwNHAJcMTZBVV3Tjrt3cMaq+sFA9/VJbgJmAT/tsF5Jknqjyyb6XYEVA/0r22FTkmRfYGvgRxOMOybJkiRLVq1atd6FSpLUN10GfCYYVlNaQLILcCbw0qq6d/z4qjqlqhZU1YJZs2atZ5mSJPVPlwG/Epgz0D8buH7YmZNsB3wOeFNVfWMj1yZJUq91GfCXAHsm2T3J1sBCYNEwM7bTfxr4cFV9osMaJUnqpc4CvqpWA8cCFwBXAh+vqqVJTkxyMECSfZKsBA4DPphkaTv7C4D9gKOSfLf927urWiVJ6psur6KnqhYDi8cNO2Gg+xKapvvx850FnNVlbZIk9Zl3spMkqYcMeEmSesiAlySphwx4SZJ6yICXJKmHDHhJknrIgJckqYcMeEmSesiAlySphwx4SZJ6yICXJKmHOr0XvTQKu8yey43XrRh1GeqLGVuRZNRVrGHnXedww8rloy5D05wBr9658boV7Hbc+aMuYw3XnnTQqEvQ+rrnbt9P2izZRC9JUg8Z8JIk9ZABL0lSDxnwkiT1kAEvSVIPGfCSJPWQAS9JUg8Z8JIk9ZABL0lSDxnwkiT1kAEvSVIPGfCSJPWQAS9JUg8Z8JIk9ZABL0lSD3Ua8EkOSHJVkmVJjp9g/H5JLk2yOsmh48YdmeSH7d+RXdYpSVLfdBbwSWYAJwMHAvOBw5PMHzfZcuAo4KPj5n0I8Bbgd4F9gbck2bGrWiVJ6psuj+D3BZZV1dVVdRdwNnDI4ARVdU1VXQbcO27eZwIXVtUtVXUrcCFwQIe1SpLUK0MFfJJPJnlWkqnsEOwKrBjoX9kO22jzJjkmyZIkS1atWjWF0iRJ6rdhA/ufgRcBP0zyriSPHGKeTDCshlzfUPNW1SlVtaCqFsyaNWvIRUuS1H9DBXxV/UdVHQE8HrgGuDDJfyV5aZKt1jLbSmDOQP9s4Poh69qQeSVJ2uIN3eSeZCeaC+JeDnwHeD9N4F+4llkuAfZMsnuSrYGFwKIhV3cB8IwkO7YX1z2jHSZJkoYw7Dn4TwFfBR4APLuqDq6qc6rqlcCDJpqnqlYDx9IE85XAx6tqaZITkxzcLnefJCuBw4APJlnaznsL8HaanYRLgBPbYZIkaQgzh5zuQ1W1eHBAkm2q6ldVtWBtM7XzLB437ISB7ktomt8nmvc04LQh65MkSQOGbaJ/xwTDvr4xC5EkSRvPOo/gk+xM8/O0+yf5Hf736vbtaJrrJUnSNDRZE/0zaS6smw28Z2D47cAbO6pJkiRtoHUGfFWdAZyR5PlV9clNVJMkSdpAkzXRv7iqzgLmJXnd+PFV9Z4JZpMkSSM2WRP9A9t/J/wpnCRJmp4ma6L/YPvv2zZNOZIkaWOYrIn+H9Y1vqpetXHLkSRJG8NkTfTf3iRVSJKkjWqYq+glSdJmZrIm+vdV1WuSfJaJH9d6cGeVSZKk9TZZE/2Z7b9/33UhkiRp45msif7b7b8Xt498fSTNkfxVVXXXJqhPkiSth6GeJpfkWcC/AD+iuR/97kn+pKo+32VxkiRp/Qz7uNh3A39QVcsAkvwW8DnAgJckaRoa9nGxN42Fe+tq4KYO6pEkSRvBZFfRP6/tXJpkMfBxmnPwhwGXdFybJElaT5M10T97oPvHwFPb7lXAjp1UJEmSNthkV9G/dFMVIkmSNp5hr6LfFjga2AvYdmx4Vb2so7okSdIGGPYiuzOBnYFnAhcDs4HbuypKkiRtmGEDfo+qejPw8/b+9M8CHtNdWZIkaUMMG/B3t//+NMmjge2BeZ1UJEmSNtiwN7o5JcmOwJuBRcCD2m5JkjQNDRXwVfWhtvNi4OHdlSNJkjaGYa+i3wl4K/BkmhvdfBV4e1X9pLvStLnYZfZcbrxuxajLkLYcM7YiyairWMPOu87hhpXLR12GBgzbRH828BXg+W3/EcA5wB92UZQ2Lzdet4Ldjjt/1GX82rUnHTTqEqRu3XP3tPrMgZ+76WjYgH9IVb19oP8dSZ7TRUGSJGnDDXsV/ZeSLExyv/bvBTRPk1unJAckuSrJsiTHTzB+myTntOO/mWReO3yrJGckuTzJlUneMJUXJUnSlm6dAZ/k9iQ/A/4E+ChwV/t3NvDaSeadAZwMHAjMBw5PMn/cZEcDt1bVHsB7gZPa4YcB21TVY4AnAH8yFv6SJGly6wz4qnpwVW3X/nu/qprZ/t2vqrabZNn7Asuq6uqqGtspOGTcNIcAZ7Td5wL7p7lypIAHJpkJ3J9mp+JnU3xtkiRtsYY9B0+Sg4H92t4vV9VkV3jsCgxeWr0S+N21TVNVq5PcBuxEE/aHADcADwBeW1W3DFurJElbuqHOwSd5F/Bq4Ir279XtsHXONsGwGnKafYF7gIcBuwOvT3Kf398nOSbJkiRLVq1aNUk5kiRtOYa9yO6PgKdX1WlVdRpwQDtsXVYCcwb6ZwPXr22atjl+e+AW4EXAv1fV3VV1E/A1YMH4FVTVKVW1oKoWzJo1a8iXIklS/w0b8AA7DHRvP8T0lwB7Jtk9ydbAQprb3A5aBBzZdh8KXFRVBSwHnpbGA4EnAv89hVolSdqiDXsO/m+A7yT5Ek2z+n7AOn+61p5TPxa4AJgBnFZVS5OcCCypqkXAqcCZSZbRHLkvbGc/Gfg34Pvt+v6tqi6b2kuTJGnLNWnAt1e1/yfNUfQ+NIF7XFXdONm8VbUYWDxu2AkD3XfS/CRu/Hx3TDRckiQNZ9KAr6pKcl5VPYH7NrFLkqRpaNhz8N9Isk+nlUiSpI1m2HPwfwD8aZJrgJ/TNNNXVT22q8IkSdL6GzbgD+y0CkmStFGtM+CTbAv8KbAHcDlwalWt3hSFSZKk9TfZOfgzaG4wcznNUfy7O69IkiRtsMma6Oe3T3QjyanAt7ovSZIkbajJjuDvHuuwaV6SpM3HZEfwj2ufBw/NlfP3b/vHrqKf7JGxkiRpBNYZ8FU1Y1MVIkmSNp6pPGxGkiRtJgx4SZJ6yICXJKmHDHhJknrIgJckqYcMeEmSesiAlySphwx4SZJ6yICXJKmHDHhJknrIgJckqYcMeEmSesiAlySphwx4SZJ6yICXJKmHDHhJknrIgJckqYcMeEmSesiAlySphzoN+CQHJLkqybIkx08wfpsk57Tjv5lk3sC4xyb5epKlSS5Psm2XtUqS1CedBXySGcDJwIHAfODwJPPHTXY0cGtV7QG8FzipnXcmcBbwp1W1F/D7wN1d1SpJUt90eQS/L7Csqq6uqruAs4FDxk1zCHBG230usH+SAM8ALquq7wFU1U+q6p4Oa5UkqVe6DPhdgRUD/SvbYRNOU1WrgduAnYDfBirJBUkuTfKXE60gyTFJliRZsmrVqo3+AiRJ2lx1GfCZYFgNOc1M4PeAI9p/n5tk//tMWHVKVS2oqgWzZs3a0HolSeqNLgN+JTBnoH82cP3apmnPu28P3NIOv7iqbq6qXwCLgcd3WKskSb3SZcBfAuyZZPckWwMLgUXjplkEHNl2HwpcVFUFXAA8NskD2uB/KnBFh7VKktQrM7tacFWtTnIsTVjPAE6rqqVJTgSWVNUi4FTgzCTLaI7cF7bz3prkPTQ7CQUsrqrPdVWrJEl901nAA1TVYprm9cFhJwx03wkctpZ5z6L5qZwkSZoi72QnSVIPGfCSJPVQp0302vh2mT2XG69bMfmEkrQpzdiK5j5l08fOu87hhpXLR13GyBjwm5kbr1vBbsedP+oy1nDtSQeNugRJo3bP3X43TTM20UuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST3UacAnOSDJVUmWJTl+gvHbJDmnHf/NJPPGjZ+b5I4kf95lnZIk9U1nAZ9kBnAycCAwHzg8yfxxkx0N3FpVewDvBU4aN/69wOe7qlGSpL7q8gh+X2BZVV1dVXcBZwOHjJvmEOCMtvtcYP8kAUjyHOBqYGmHNUqS1EtdBvyuwIqB/pXtsAmnqarVwG3ATkkeCBwHvG1dK0hyTJIlSZasWrVqoxUuSdLmrsuAzwTDashp3ga8t6ruWNcKquqUqlpQVQtmzZq1nmVKktQ/Mztc9kpgzkD/bOD6tUyzMslMYHvgFuB3gUOT/C2wA3Bvkjur6gMd1itJUm90GfCXAHsm2R24DlgIvGjcNIuAI4GvA4cCF1VVAU8ZmyDJW4E7DHdJkobXWcBX1eokxwIXADOA06pqaZITgSVVtQg4FTgzyTKaI/eFXdUjSdKWpMsjeKpqMbB43LATBrrvBA6bZBlv7aQ4SZJ6zDvZSZLUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMzR13AdLbL7LnceN2KUZchSVofM7YiyairWMPOu87hhpXLN8m6DPh1uPG6Fex23PmjLmMN15500KhLkKTNwz13b9Hf4TbRS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDnQZ8kgOSXJVkWZLjJxi/TZJz2vHfTDKvHf70JN9Ocnn779O6rFOSpL7pLOCTzABOBg4E5gOHJ5k/brKjgVurag/gvcBJ7fCbgWdX1WOAI4Ezu6pTkqQ+6vIIfl9gWVVdXVV3AWcDh4yb5hDgjLb7XGD/JKmq71TV9e3wpcC2SbbpsFZJknqly4DfFRh8FNvKdtiE01TVauA2YKdx0zwf+E5V/aqjOiVJ6p0unyY30TP6airTJNmLptn+GROuIDkGOAZg7ty561elJEk91OUR/EpgzkD/bOD6tU2TZCawPXBL2z8b+DTwkqr60UQrqKpTqmpBVS2YNWvWRi5fkqTNV5cBfwmwZ5Ldk2wNLAQWjZtmEc1FdACHAhdVVSXZAfgc8Iaq+lqHNUqS1EudBXx7Tv1Y4ALgSuDjVbU0yYlJDm4nOxXYKcky4HXA2E/pjgX2AN6c5Lvt3290VaskSX3T5Tl4qmoxsHjcsBMGuu8EDptgvncA7+iyNkmS+sw72UmS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPWTAS5LUQwa8JEk9ZMBLktRDBrwkST1kwEuS1EMGvCRJPbIdFF8AAAdXSURBVGTAS5LUQwa8JEk91GnAJzkgyVVJliU5foLx2yQ5px3/zSTzBsa9oR1+VZJndlmnJEl901nAJ5kBnAwcCMwHDk8yf9xkRwO3VtUewHuBk9p55wMLgb2AA4B/apcnSZKG0OUR/L7Asqq6uqruAs4GDhk3zSHAGW33ucD+SdIOP7uqflVV/wMsa5cnSZKG0GXA7wqsGOhf2Q6bcJqqWg3cBuw05LySJGktUlXdLDg5DHhmVb287f9jYN+qeuXANEvbaVa2/T+iOVI/Efh6VZ3VDj8VWFxVnxy3jmOAY9reRwBXdfJiNtxDgZtHXcRmwO00HLfTcNxOk3MbDWc6b6fdqmrWRCNmdrjSlcCcgf7ZwPVrmWZlkpnA9sAtQ85LVZ0CnLIRa+5EkiVVtWDUdUx3bqfhuJ2G43aanNtoOJvrduqyif4SYM8kuyfZmuaiuUXjplkEHNl2HwpcVE2TwiJgYXuV/e7AnsC3OqxVkqRe6ewIvqpWJzkWuACYAZxWVUuTnAgsqapFwKnAmUmW0Ry5L2znXZrk48AVwGrgz6rqnq5qlSSpb7psoqeqFgOLxw07YaD7TuCwtcz7TuCdXda3CU370wjThNtpOG6n4bidJuc2Gs5muZ06u8hOkiSNjreqlSSphwz4DiWZk+RLSa5MsjTJq0dd03SVZEaS7yQ5f9S1TFdJdkhybpL/bt9TTxp1TdNRkte2n7fvJ/lYkm1HXdN0kOS0JDcl+f7AsIckuTDJD9t/dxxljdPBWrbT37Wfu8uSfDrJDqOscVgGfLdWA6+vqkcBTwT+bILb9arxauDKURcxzb0f+PeqeiTwONxe95FkV+BVwIKqejTNBb4LR1vVtHE6za2/Bx0PfLGq9gS+2PZv6U7nvtvpQuDRVfVY4AfAGzZ1UevDgO9QVd1QVZe23bfTfCF7R75xkswGngV8aNS1TFdJtgP2o/nlCVV1V1X9dLRVTVszgfu399Z4ABPcQ2NLVFVfofm10qDB24WfATxnkxY1DU20narqC+3dVgG+QXNvlmnPgN9E2ifl/Q7wzdFWMi29D/hL4N5RFzKNPRxYBfxbeyrjQ0keOOqippuqug74e2A5cANwW1V9YbRVTWu/WVU3QHNAAvzGiOvZHLwM+PyoixiGAb8JJHkQ8EngNVX1s1HXM50kOQi4qaq+PepaprmZwOOBf66q3wF+js2p99GeQz4E2B14GPDAJC8ebVXqiyR/RXPq9SOjrmUYBnzHkmxFE+4fqapPjbqeaejJwMFJrqF54uDTkpw12pKmpZXAyqoaawE6lybwtaY/BP6nqlZV1d3Ap4D/M+KaprMfJ9kFoP33phHXM20lORI4CDiiNpPflxvwHWoffXsqcGVVvWfU9UxHVfWGqppdVfNoLoa6qKo84hqnqm4EViR5RDtof5o7PWpNy4EnJnlA+/nbHy9GXJfB24UfCXxmhLVMW0kOAI4DDq6qX4y6nmEZ8N16MvDHNEel323//mjURWmz9UrgI0kuA/YG/nrE9Uw7bQvHucClwOU033Gb5V3INrYkHwO+DjwiycokRwPvAp6e5IfA09v+LdpattMHgAcDF7bf4/8y0iKH5J3sJEnqIY/gJUnqIQNekqQeMuAlSeohA16SpB4y4CVJ6iEDXtoCJJmd5DPtU8N+lOT9SbaeZJ43bqr6JG18BrzUc+0NXz4FnNc+Ney3gQcB75xkVgNe2owZ8FL/PQ24s6r+DaCq7gFeC7wsySuSfGBswiTnJ/n9JO+ieSLbd5N8pB33kvZ52N9LcmY7bLckX2yHfzHJ3Hb46Un+OcmXklyd5Kntc7avTHL6wPqekeTrSS5N8on2uQ0keVeSK9rl/v0m2k5Sr8wcdQGSOrcXsMbDfKrqZ0mWs5bvgKo6PsmxVbU3QJK9gL8CnlxVNyd5SDvpB4APV9UZSV4G/AP/+8jRHWl2Lg4GPktzZ8eXA5ck2Zvm/vpvAv6wqn6e5Djgde0Ox3OBR1ZVJdlhI20HaYtiwEv9F2CiW1aubfhEngacW1U3A1TV2POynwQ8r+0+E/jbgXk+2wb05cCPq+pygCRLgXk0z9SeD3ytOYvA1jS3CP0ZcCfwoSSfA84fskZJAwx4qf+WAs8fHJBkO2AOcBtrnqrbdi3LGHZnYHCaX7X/3jvQPdY/E7gHuLCqDr/PypJ9aR4UsxA4lmYHQ9IUeA5e6r8vAg9I8hKAJDOAdwOnA1cDeye5X5I5wL4D893dPu54bBkvSLJTu4yxJvr/oglhgCOA/5xCXd8Anpxkj3aZD0jy2+15+O2rajHwGpoH60iaIo/gpZ5rm8mfC/xTkjfT7NgvprlK/i7gf2ievPZ9mqewjTkFuCzJpVV1RJJ3AhcnuQf4DnAU8CrgtCR/AawCXjqFulYlOQr4WJJt2sFvAm4HPpNkW5qWg9eu3yuXtmw+TU6SpB6yiV6SpB4y4CVJ6iEDXpKkHjLgJUnqIQNekqQeMuAlSeohA16SpB4y4CVJ6qH/DxqtgC1UQ8bMAAAAAElFTkSuQmCC\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Show the distribution of probabilities for flipping two dice\n", "x = [k for k in range(2,13)]\n", "y = [1/36,2/36,3/36,4/36,5/36,6/36,5/36,4/36,3/36,2/36,1/36]\n", "\n", "plt.figure(num=None, figsize=(8, 6))\n", "plt.bar(x,y, width=1.0,edgecolor='black')\n", "plt.title('Probability Distribution for Tossing Two Dice')\n", "plt.ylabel(\"Probability\")\n", "plt.xlabel(\"Outcomes\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### TODO (no credit, but don't skip this)\n", "\n", "Notice the line starting `plt.figure( ... )`. Try changing the numbers for the `figsize` and see what happens.\n", "Which one is the width and which is the height?" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Histograms\n", "\n", "A histogram is a visualization of the frequency (the count) of various outcomes from an experiment or a process. The X-axis\n", "gives the outcomes, and the Y-axis gives the frequency (count) of each outcome. \n", "\n", "\n", "- If you give a list of values to hist(...) it will create a histogram counting how many of each value occur; this list can be unordered;\n", "- You will get a cleaner display if you specify where the edges of the bins are, and make sure the edges of the bins are visible, as shown in this example:" ] }, { "cell_type": "code", "execution_count": 83, "metadata": { "scrolled": false }, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(num=None, figsize=(8, 6))\n", "plt.hist([1,2,4,2,6,2,4,5,6,4,6,3,4,3],bins=[0.5,1.5,2.5,3.5,4.5,5.6,6.5],edgecolor='black')\n", "plt.title('Sample Histogram')\n", "plt.xlabel(\"Outcomes\")\n", "plt.ylabel(\"Frequency\")\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Problem 2: Displaying the results of a random experiment using histograms\n", "Read and understand the function dieRoll(num_trials) below, which simulates the experiment of rolling a fair, six-sided die num_trials times. \n", "- The outcomes are $\\{1,2,3,4,5,6\\}$ (we will call this the *sample space* next week); \n", "- The probability of any particular outcome is $\\frac{1}{6}$.\n", "- If we record the outcome for a large number of experiments, we would expect the number of outcomes to be \"evenly distributed\" (next week we'll call this \"equi-probable\"). In other words, for a large number of trials, we would expect the probability of each outcome $k\\in \\{1,2,3,4,5,6\\}$ to be\n", "\n", "$$\\frac{\\text{number of times we observed a value } k}{\\texttt{num_trials}} \\approx \\frac{1}{6}$$ \n", "\n", "First, we will learn how to generate random integer values. " ] }, { "cell_type": "code", "execution_count": 84, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "0" ] }, "execution_count": 84, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# Demo of randint(lo,hi), which generates a random integer from the sequence \n", "# [lo,lo+1,...,hi-1]. Note carefully that the lower bound is inclusive and the upper bound is non-exclusive, just\n", "# like the range(...) function in Python. \n", "\n", "# Run this cell a few times!\n", "\n", "randint(0,4)" ] }, { "cell_type": "code", "execution_count": 85, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "array([3, 1, 0, 3, 3, 3, 3, 1, 3, 1])" ] }, "execution_count": 85, "metadata": {}, "output_type": "execute_result" } ], "source": [ "# You can also ask it for an array of a given size, since it is a Numpy function:\n", "\n", "randint(0,4,10)" ] }, { "cell_type": "code", "execution_count": 86, "metadata": {}, "outputs": [], "source": [ "# Ok, your turn!\n", "\n", "# Write a function which simulates rolling a fair die num_trials times, i.e., a number is selected from \n", "# (1,2,3,4,5,6) with equal probability num_trials times. By default, num_trials is set to 100000.\n", "\n", "\n", "\n", "seed(0)\n", "\n", "def roll_die(num_trials = 100000): # Notice the use of a default value for the parameter here\n", "\n", " # this creates a 1D array of length num_trials of random integers 1..6\n", "\n", " return [ ] # <= Your code here\n", "\n", "example_trials = roll_die()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Next, provide code in the next cell which will show the result of this experiment. Be sure to provide appropriate values for `bins` which give the edges of the six bins. " ] }, { "cell_type": "code", "execution_count": 87, "metadata": {}, "outputs": [], "source": [ "# Solution: \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Counting the frequency of an outcome using a Python dictionary\n", "\n", "A dictionary is a data structures which stores (key,value) pairs (typically implemented as a hash table).\n", "This is a great data structure for storing information about objects without having to muck around with lists.\n" ] }, { "cell_type": "code", "execution_count": 88, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "{'a': 2, 'c': 8, 'b': 1}\n", "2\n" ] } ], "source": [ "D = { 'a' : 2, 'c' : 8, 'b' : 1} # Dictionary storing, say, how many times a letter appears in a string\n", "print(D)\n", "print(D['a'])" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The `Counter` function creates a dictionary of frequency counts from a list of outcomes. " ] }, { "cell_type": "code", "execution_count": 89, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Counter creates a dictionary giving the frequency counts of each element in the list:\n", "Counter({3: 5, 4: 5, 2: 2, 5: 2, 8: 1})\n", "\n", "The list has 5 instances of the number 3.\n" ] } ], "source": [ "### Calculating frequency counts using a dictionary\n", "\n", "#from collections import Counter <- this was imported in the first code cell\n", "\n", "F = Counter([3,4,2,3,4,5,4,3,2,3,4,5,4,3,8])\n", "\n", "print(\"Counter creates a dictionary giving the frequency counts of each element in the list:\")\n", "print(F)\n", "\n", "print()\n", "\n", "n = 3\n", "print(\"The list has\",F[n], 'instances of the number '+ str(n) + '.')\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Problem 3: Displaying the distribution of random outcomes\n", "\n", "Now we will display the same results as in Problem 2, but showing the distribution of probabilities, instead of an explicit histogram. The only important difference in the data visualization is that the Y-axis gives the probability instead of the frequency count. Essentially, you have to divide each frequency count by the total number of outcomes involved. \n", "\n", "You will use the funtion bar(...) demonstrated above, after using Counter to find the frequency counts explicitly. Then you simply divide by the total number of outcomes to get the probability. \n", "\n", "TO DO: Complete the function stub below which takes the list returned by roll_die(...), or any other experiment returning numerical results, and produces a frequency distribution; this should have the same shape as the histogram, but the Y axis will be probabilities instead of the frequency. Again, create appropriate labels. Demonstrate your function, again, on the list example_trials produced in Problem 2. " ] }, { "cell_type": "code", "execution_count": 90, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Solution \n", "\n", "seed(0) # NEVER put the seed(0) line inside a function! If you do, you can't call it more than once. \n", "\n", "def show_distribution(outcomes, title='Probability Distribution'):\n", " num_trials = len(outcomes)\n", " X = [ ] # <= Your code here .. Hint: Use an appropriate range(...) function\n", " Y = [ ] # <= Your code here\n", " plt.bar(X,Y,width=1.0,edgecolor='black')\n", " plt.xlabel(\"Outcomes\")\n", " plt.ylabel(\"Probability\")\n", " plt.title(title)\n", " plt.show()\n", "\n", "\n", "show_distribution(example_trials,title='Probability Distribution for Single Die Toss')\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Motivation for Monte Carlo simulation\n", "For the case of a fair die, the distribution is very easily computed. In general, it is very difficult to write down a closed form solution for the distribution of real world events. This is where simulation comes into play-- instead of mathematically computing the distribution explicitly, you can use this method of repeating experiments, and recording outcomes to understand the probabilistic rules governing some real world event. When you can come up with an analytical result, this is a nice way of confirming its correctness!" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Problem 4\n", "You will now do the same thing you did in the previous problems, but with a new experiment: instead of rolling one die and recording the value, you will simulate rolling $n$ dies and recording their sum. For example, if $n=2$ and the first die shows up as a 3, and the second die shows up as a 1, the sum (and the outcome we store) would be 4. \n", "\n", "TO DO: Complete the function stub below and then demonstrate by providing the single line of code which would print out the probability distribution for rolling 2 dice 100,000 times. \n", "\n", "Hint: Not required, but think about how you might do this in one line using Numpy and list comprehensions. " ] }, { "cell_type": "code", "execution_count": 91, "metadata": {}, "outputs": [], "source": [ "# Perform the experiment using the following function. \n", "# Recall that randint(a,b) uniformly and randomly selects an integer x such that a<= x < b\n", "# The second argument determines the length of the result. In this case, we only need\n", "# a one dimensional array (a list)\n", "\n", " \n", "seed(0)\n", " \n", "# Solution\n", "def roll_and_add_dice(num_dice, num_trials = 10**5):\n", "\n", " pass # Your code here\n", " \n", "\n", "\n", "\n", "# You could also do it in a single line with a list comprehension! See if you can figure that out!\n" ] }, { "attachments": { "Screen%20Shot%202019-09-07%20at%202.47.57%20PM.png": { "image/png": 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" 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" } }, "cell_type": "markdown", "metadata": { "collapsed": true }, "source": [ "# Problem 5 (Monte Carlo Calculation of $\\pi$)\n", "\n", "This final problem is also a Monte Carlo simulation, but this time in\n", "the continuous domain: we will calculate the value of $\\pi$ using\n", "a variation of Problem 1B. \n", "\n", "We will leave this one up to you as it the exact details, but you must\n", "use the following fact: a circle inscribed in a unit square (i.e., with\n", "side of length and area 1.0):\n", "\n", "![Screen%20Shot%202019-09-07%20at%202.47.57%20PM.png](attachment:Screen%20Shot%202019-09-07%20at%202.47.57%20PM.png)\n", "\n", "has as radius of 0.5 and an area of $\\pi\\ast (0.5^2) = \\frac{\\pi}{4}.$\n", "\n", "Therefore, if you generate num_trials random points in the unit square, as in Problem 1B,\n", "and count how many land inside the circle, you can calculate an approximation of $\\pi$. \n", "\n", "For this problem, you must\n", "
\n", "\n", " (A) Draw the diagram of the unit square with inscribed circle, and then draw 500 random points, and calculate the value of $\\pi$; \n", " \n", " (B) Without drawing the diagram, calculate the value of $\\pi$ you would get\n", " from $10^5$ trials. \n", " \n", "[Optional!] After completing (B), try to get a more accurate value for $\\pi$ by increasing the number of trials. Your results will depend on your machine, but for comparison, with my new Macbook Pro with the M1 chip, I ran it with $10^8$ trials while I got a cup of coffee, and it had the answer correct to 3 decimal places. Sometimes I have run big experiments overnight! \n", " \n", "
\n", "Hint: Start by copying your code from Problem 1B. You might find Mr. Pythagoras's formula useful. \n", "To draw the inscribed circle, consider the code from \"A Smooth-Looking Curve\" at the top of\n", "this notebook: create a sequence of values (representing the angle theta in radians):\n", "
\n", " thetas = np.linspace(0, 2*np.pi, 100)\n", "
\n", " Then to create the x and y values for the points around the circle, you can use\n", " the np.sin(...) and np.cos(...) functions, following the typical diagram \n", " about unit circles and trig functions:\n", " \n", " ![Screen%20Shot%202020-01-28%20at%204.08.20%20PM.png](attachment:Screen%20Shot%202020-01-28%20at%204.08.20%20PM.png)\n", " \n", " \n", " (see https://www.mathsisfun.com/geometry/unit-circle.html for more explanation). " ] }, { "cell_type": "code", "execution_count": 92, "metadata": {}, "outputs": [], "source": [ "# (A)\n", "\n" ] }, { "cell_type": "code", "execution_count": 93, "metadata": {}, "outputs": [], "source": [ "# (B)\n", "\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": "3.7.6" } }, "nbformat": 4, "nbformat_minor": 2 }