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"# CS 237 Spring 2021, HW 12 \n",
"\n",
"#### Due date: Friday April 30rd at Midnight (1 minute after 11:59pm on 4/30) via Gradescope (with a 6 hour grace period)\n",
"\n",
" Late policy: You may submit the homework up to 24 hours late for a 10% penalty. Hence, the late deadline is Saturday 5/1 at Midnight (with a 6 hour grace period). \n",
"\n",
"#### General Instructions\n",
"\n",
"Please complete this notebook by filling in solutions where indicated. \n",
"\n",
"For full credit, please take careful note of the following requirements:\n",
"\n",
"- Do NOT use any HTML tags in your notebook, as Gradescope will ignore them;\n",
"\n",
"- Do NOT answer questions by including images, as Gradescope will ignore them; and \n",
"\n",
"- You MUST \"Restart and Run All\" from the Kernel menu before submitting to Gradescope.\n",
"\n",
"- You must present all numbers in readable form (approximately 4 digits of precision) unless otherwise stated. \n",
"\n",
"**Any assignments which do not follow these requirements will not receive full credit.** \n",
"\n",
"\n",
"There are 10 problems on this exam, 6 analytical, 3 lab problems (7, 8, and 9), and one\n",
"problem on Linear Regression, which we will cover in lecture on Tuesday, 4/27. "
]
},
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"\n"
]
}
],
"source": [
"# General useful imports\n",
"import numpy as np\n",
"from numpy import arange,linspace,mean, var, std, corrcoef, transpose, ones,log\n",
"from numpy.linalg import inv\n",
"import matplotlib.pyplot as plt\n",
"from mpl_toolkits.mplot3d import Axes3D\n",
"import matplotlib.mlab as mlab\n",
"from numpy.random import seed,random, randint, uniform\n",
"import math\n",
"from collections import Counter\n",
"import pandas as pd\n",
"%matplotlib inline\n",
"\n",
"\n",
"from math import log, pi, log, floor, ceil, sqrt # import whatever you want from math\n",
"\n",
"from scipy.special import comb\n",
" \n",
"def C(N,K): \n",
" return comb(N,K,True) # just a wrapper around the scipy function\n",
"\n",
"\n",
"# Here are the basic statistical functions we will use from numpy\n",
"\n",
"from numpy import mean, var, std, median\n",
"\n",
"L = [2,4,3,6,4,5]\n",
"\n",
"# mean value\n",
"\n",
"mean(L) \n",
"\n",
"\n",
"# Variance\n",
"# ddof = delta degrees of freedom, default is 0\n",
"\n",
"# population variance\n",
"var(L) \n",
"\n",
"# sample variance\n",
"var(L,ddof=1)\n",
"\n",
"# Standard deviation\n",
"# ddof = delta degrees of freedom, default is 0\n",
"\n",
"# population standard deviation\n",
"std(L) \n",
"\n",
"# sample standard deviation\n",
"std(L,ddof=1) \n",
"\n",
"# Median\n",
"\n",
"median(L) \n",
"\n",
"# Random sampling of `size` elements from list with or without replacement\n",
"\n",
"np.random.choice(L,size=1,replace=True)\n",
" \n",
"# Scipy statistical functions\n",
"\n",
"from scipy.stats import norm, binom, expon, geom, poisson, gamma, nbinom, bernoulli,uniform \n",
"\n",
"# https://docs.scipy.org/doc/scipy/reference/stats.html\n",
"\n",
"#### Normal Distribution #####\n",
"\n",
"###### Note that in this library loc = mean and scale = standard deviation #####\n",
"\n",
"# Examples assume random variable X (e.g., housing prices) normally distributed with mu = 60, sigma = 10\n",
"\n",
"# Probability Density Function (really only useful for drawing the curve)\n",
"# f(x) = P(X == x)\n",
"\n",
"norm.pdf(x=50,loc=60, scale= 10) \n",
"\n",
"# Cumulative Density Function\n",
"# F(x) = P(X < x)\n",
"\n",
"# Example: Percentage of houses less than 50K. \n",
"norm.cdf(x=50,loc=60,scale=10) \n",
"\n",
"# Example: Find P(60
(A) What is the probability that 12 patients arrive between 6am and 7am?
\n", "(B) What is the probability that no patient arrives before 7am?
\n", "(C) What is the probability that the first patient arrives between 6am and 7am?
\n", "(D) What is the probability that the first patient arrives between 6:15 and 6:45?
\n", "(E) Suppose it is 6:15 and no patient has arrived yet; now what is the probability that the first patient arrives between 6:15 and 6:45?
\n", "Hint: Use the Poisson for (A) and (B) and the Exponential for (C), (D), and (E). \n", "Note carefully how (D) and (E) are different: in (D) it is possible that the first patient arrives between 6am and 6:15am, whereas for (E) you know this has not happened. \n", "The result for the two will be different!\n", "\n", "
" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**" ] }, { "attachments": { "Screen%20Shot%202021-04-23%20at%209.30.15%20AM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Four (Joint Random Variables)\n", "\n", "\n", "\n", "Suppose we roll two three-sided dice (having sides with 1, 2, or 3 dots showing, or with numbers as shown above). Let $X$ indicate the sum of the dots/numbers on the two dice, and $Y$ indicate the absolute value of the difference in the dots/numbers showing on each die. For example, if the first die lands 2 and the second die lands 1, then X would return 3 and Y would return 1. \n", "\n", "(A) Calculate the joint probability mass function for $(X,Y)$ and show marginal probabilities for $X$ and $Y$. \n", "\n", "Show your results in some suitable form using a matrix drawn in text or using Markdown tables, as shown in the Markdown Tutorial posted on the class web site (the section on tables is at the very end). Use the format\n", "shown in the lecture slides for Lecture 21 as a model for how to present your results.\n", "\n", "DO NOT include an image file, as we can not view it in Gradescope. \n", "\n", "(B) Calculate $E(X)$, $\\sigma_X$, $E(Y)$, and $\\sigma_Y$. \n", "\n", "(C) Calculate $Cov(X,Y)$ and the correlation coefficient $\\rho_{X,Y}$.\n", "\n", "(D) Are these two random variables independent? (Answer Yes or No and explain briefly.) \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Five (Independent Joint Random Variables)\n", "\n", "From an ordinary deck of 52 cards, 8 cards are drawn at random and without replacement. Let $X$ and $Y$ be the number of clubs and the number of spades, respectively. Are $X$ and $Y$ independent?\n", "\n", "Hint: Rather than draw out the whole matrix, just use the fact that $X$ and $Y$ are independent iff\n", "\n", "$$P(X\\,\\vert\\, Y = k ) = P(X)\\quad\\text{for all $k$, }\\ 0\\le k\\le 8.$$\n", "\n", "Investigate whether this is true for various values of $k$, starting with $k=8$. OR, just check these cells in the matrix and see if you can find a counter-example. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Lab Problems (6, 7, and 8)\n", "\n", "The lab problems will use various display functions given in the first code cell of this document. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Six -- Scatterplots of Continuous Bivariate Data\n", "\n", "First we will consider how to create *scatterplots* of random data in 2D dimensions, starting with continuous data points. We will use points from the uniform distribution over [0..10), and also the normal and exponential. \n", "\n", "### Part A\n", "\n", "Apply the function `display2DScatterAndMarginals` to create a scatterplot of $10^4$ random points (x,y) uniformly distributed over the range $[0,10)\\times [0,10)$ using the function:\n", "\n", "> uniform.rvs(lower_bound,upper_bound, size=num_trials).\n" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "\n", " (i) Just looking at the graphical display of the data, would you think there is\n", " a linear trend to this data, i.e., is there a correlation between\n", " GPA and homework scores in CS 237? What do you see?\n", "\n", "\n", "
\n", " (ii) Now, what does the $R^2$ value tell you about fitting a linear model to this data?\n", "\n", "\n", "Linear regression isn't always appropriate, and not only because of the $R^2$ score. Please read through the following page outlining the principal conditions necessary for linear regression:\n", "\n", "https://www.statisticshowto.datasciencecentral.com/assumptions-conditions-for-regression/\n", "\n", "
\n", " (iii) Do you see any other problems, related to the conditions you read about above? (Hint: look at the residual plot).) Can you think of any reason why this might be the case for this data set? (Hint: Just answer these by \"eyeballing\" the data, don't worry about doing a precise analysis.)\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": "3.8.5" } }, "nbformat": 4, "nbformat_minor": 2 }