{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# CS 237 Spring 2021, HW 09 \n", "\n", "#### Due date: Thursday April 8th at Midnight (1 minute after 11:59pm on 4/8) 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 Friday 4/9 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", "**Any assignments which do not follow these requirements will not receive full credit.** \n", "\n", "\n", "\n", "There are 8 problems on this homework, the last of which is a \"lab\" problem; many will involve using Python to solve, using the functions in the next code cell. Each problem is worth 7.5 points. An introductory video will be posted on YT for\n", "the analytical problems, and the lab problem will be covered Friday in lab. " ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n" ] } ], "source": [ "# Here are some imports which will be used in code that we write for CS 237\n", "\n", "import matplotlib.pyplot as plt # normal plotting\n", "import numpy as np\n", "\n", "from math import log, pi, log, floor, ceil, sqrt # import whatever you want from math\n", "from random import seed, random\n", "from collections import Counter\n", "\n", "%matplotlib inline\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 \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 x)\n", "\n", "# Example: Percentage of houses more than 50K.\n", "norm.sf(x=50,loc=60,scale=10) \n", "\n", "# Percentage Point Function: Inverse of the CDF:\n", "# For what is the largest value of k for which P( X < k ) = q ?\n", "\n", "# Example: What is the maximum cost of the 5% cheapest houses, \n", "# i.e., the x such that P(X < x) = 0.05?\n", "\n", "norm.ppf(q=0.05,loc=60,scale=40)\n", "\n", "# Inverse Survival Function: Inverse (1 - CDF):\n", "# For what is the smallest value of k for which P( X > k ) = q ?\n", "\n", "# Example: What is the minimum cost of the 5% most expensive houses, \n", "# i.e., the x such that P(X > x) = 0.05?\n", "\n", "norm.isf(q=0.05,loc=60,scale=40)\n", "\n", "# Give the endpoints of the interval (centered on the mean)\n", "# which contain alpha/100 percent of the population (alpha is a probability)\n", "\n", "# Ex. Give the interval for the middle 75% of the houses\n", "\n", "norm.interval(alpha=0.75, loc=60, scale=40)\n", "\n", "# generate a random variate\n", "norm.rvs(loc=60, scale=40)\n", "\n", "# generate random variates, returns list of length = size\n", "norm.rvs(loc=60, scale=40, size=10)\n", "\n", "\n", "\n", "\n", "##### Bernoulli Distribution X ~ Bernoulli(p) ####\n", "\n", "# p = probability of success for Bernoulli trial\n", "\n", "# Generate a random variate\n", "bernoulli.rvs(p=0.5)\n", "\n", "# Generate a list of random variates\n", "bernoulli.rvs(p=0.5,size=100)\n", "\n", "##### Binomial Distribution X ~ B(n,p) ####\n", "\n", "# n = number of independent Bernoulli trials\n", "# p = probability of success for Bernoulli trial\n", "# k = outcome in range [0 .. n]\n", "\n", "# Generate a random variate\n", "binom.rvs(n=10, p=0.5)\n", "\n", "# Generate a list of random variates\n", "binom.rvs(n=10, p=0.5,size=100)\n", "\n", "# Probability mass function.\n", "binom.pmf(k=4, n=10, p=0.5)\n", "\n", "# Cumulative distribution function\n", "binom.cdf(k=4, n=10, p=0.5)\n", "\n", "print() " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem One\n", "\n", "Suppose that Wayne and Liz agree to meet at Starbucks on Comm Ave sometime between\n", "1pm and 2pm. Each will show up at a time between 1pm and 2pm independently and equiprobably in that interval. Each will wait at most 15 minutes for the other and then leave. \n", "What is the probability that they will in fact meet?\n", "\n", "Hint: Draw a square with the times from 1 - 2pm on each side. The random event of their arrival times is a point inside this square. Find the regions for when they will meet, and when they will not, and determine the probability from the areas. \n", "\n", "You do not need to provide the diagram in your answer, but do provide some\n", "explanation of your method for determining the answer. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Two\n", "\n", "(Continuous Distributions) Let X be a continuous random variable with a frequency distribution (PMF) of the form \n", "\n", "$$ f(x) =\n", "\\begin{cases}\n", " {\\large\\frac{x}{4}} & \\text{if $1\\le x\\le 3$} \\\\[4pt]\n", " \\,0 & \\text{otherwise} \\\\\n", "\\end{cases}$$\n", " \n", "which can be graphed as follows:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 5))\n", "plt.title(\"PDF for Problem Two\")\n", "X = np.linspace(0,4,1000)\n", "plt.plot(X,[x/4 if 1 <= x <= 3 else 0 for x in X])\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ " (A) Determine the formula for the CDF $F_X$ using geometrical techniques (i.e., not using integrals, but considering what happens to the area to the left of a point $a$ by considering the area of geometrical shapes)\n", " \n", " (B) Determine the formula for the CDF $F_X(x)$ using an integral. \n", " \n", " (C) Plot the CDF $F_X(x)$ (using the code above as a model).\n", " \n", " (D) Find $P(X\\ge 2)$ \n", " \n", " (E) Find $E(X)$ \n", " \n", "Show all work for full credit. \n", "\n", "For (D) -- (E) you must use mathematical techniques and not just calculate it using iterative techniques in Python code. You may use Python to calculate results of mathematical formulae. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Three\n", "\n", "The time elapsed, in minutes, between the placement of an order for pizza and its delivery at a particular shop is a uniform RV, with the density function\n", "\n", "\n", "$$\\begin{equation}\n", " f(x) = \\begin{cases}\n", " 1/15 & \\text{if } 25" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def f4(x):\n", " if x < 1 or x > 2:\n", " return 0\n", " else:\n", " return 2.0/(x**2)\n", "\n", "X = np.linspace(0,3,100)\n", "Y = [f4(x) for x in X]\n", "\n", "plt.figure(figsize=(8, 5))\n", "plt.title(\"PDF for Problem Four\")\n", "plt.plot(X,Y)\n", "plt.show()" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "# Scipy.stats \n", "\n", "For the following, use the statistical functions given at the top of this notebook. \n", "\n", "Also consider using the Distributions Notebook posted online to visualize these distributions (but use scipy.stats for the calculations). \n", "\n", "You are not required to do so, but a nice touch is to print out your answer in a code block, i.e., if\n", "you were asked \"What is the probability in the standard normal that a value occurs in the interval between\n", "-0.94 and 1.2 standard deviations from 0,\" you could answer as follows:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Solution: 0.7113\n" ] } ], "source": [ "mu = 0\n", "sigma = 1\n", "lo = -0.94\n", "hi = 1.2\n", "\n", "answer = norm.cdf(x=hi,loc=mu,scale=sigma) - norm.cdf(x=lo,loc=mu,scale=sigma)\n", "print(\"Solution: \" + str(np.around(answer,4)))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Five (Normal Distribution)\n", "\n", "Suppose that in a population of individuals, their height is normally distributed with a mean $\\mu =68$ inches and a standard deviation of $\\sigma=1.45$ inches.

\n", "\n", "

(A) \n", " What is the probability that a randomly-selected individual has a height less than 66 inches?

\n", " \n", "

(B) What is the probability that a randomly-selected individual has a height more than 72 inches?

\n", "\n", "

(C) What is the probability that a randomly-selected individual has a height between 66.5 and 71 inches?

\n", "\n", "

(D) What is the maximum height for a person to be in the bottom 1% of the population in terms of height?

\n", "\n", "

(E) To characterize the \"middle 50%\" of the population in terms of the standard deviation, give the value $k$ in this formula:\n", " \n", "$$P( | X - \\mu_X | < k\\cdot\\sigma_X ) = 0.5.$$\n", "\n", "Note that this does not depend on the exact values for $\\mu$ and $\\sigma$ given in this problem. \n", "

\n", "\n", "Hint: peruse the functions from the `norm` library given in the first code cell above. \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "![](hw07.4c.png)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n" ] }, { "attachments": { "Screen%20Shot%202020-03-20%20at%205.33.58%20PM.png": { "image/png": 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" } }, "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Six (Truncated Normal Distribution)\n", "\n", "The problem with grades is that they are usually normally distributed, but\n", "of course grades can not be any real number, but have upper and lower bounds. Here is a chart of GPAs of 4897 students at a modern university currently on lockdown:\n", "\n", "![Screen%20Shot%202020-03-20%20at%205.33.58%20PM.png](attachment:Screen%20Shot%202020-03-20%20at%205.33.58%20PM.png)\n", "\n", "The problem with this, of course, is that a normal distribution seems to fit, but it is truncated at the highest value of 4.0. How do we deal with this kind of distribution? Hm... it looks like we need to *condition* the problem so that we are only looking at that part of the distribution in the range [0..4], that is\n", "\n", "$$P( \\,\\, \\ldots X \\ldots \\,\\,|\\,\\, 0\\le X \\le 4 \\,\\,)$$ \n", "\n", "(realistically you can ignore $X<0$). \n", "\n", "Let us suppose that a normal distribution with mean $mu=3.3$ and variance $\\sigma^2=0.4$ describes the overall curve before it was truncated at 4.0 (and 0.0). \n", "\n", "Browse the functions from scipy.stats.norm given in the first code cell above to see which one will solve each problem. \n", "\n", "(A) The BA/MS program requires a 3.0 GPA to apply. What percentage of this group\n", "would be eligible to apply?\n", "\n", "(B) Approximately how many students are below 2.0? (Hint: I mean the actual number of students, not the percentage; figure out the percentage of the total, and round to the nearest integer). \n", "\n", "(C) Latin Honors at this school are calculated as follows:\n", "\n", "![Screen%20Shot%202020-03-20%20at%206.15.35%20PM.png](attachment:Screen%20Shot%202020-03-20%20at%206.15.35%20PM.png)\n", "\n", "What are the GPA cutoffs for each of these honors?\n", "\n", "Hint for (C): You must reduce the percentages appropriately, since you are looking for\n", "a percentage of the values below 4.0. For example, for Summa, you are looking\n", "for $k$ such that\n", "\n", "$$P(\\,k4)$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Solution:" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Seven (Combining Normal with Other Distributions)\n", "\n", "Suppose that in the Men's Olympic Ski Team, the chest size measurements are normally distributed with a mean of 39.8 inches and a standard deviation of 2.05 inches.\n", "\n", "\n", "(A) What the probability that of 20 randomly selected members of the team, at least 5 have a chest size of at least 41.7 inches?\n", "\n", "(B) Supposing we choose men on the team repeatedly and with replacement, how many men would you expect to choose before finding a member with a chest measurement of less than 37 inches?\n", "\n", "Hint: Let X is a normally distributed random variable according to the parameters given in the first sentence. Then consider Y and Z be appropriately distributed random variables for (A) and (B) respectively. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:**\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Generating Variates from a Continuous Distribution\n", "\n", "Samples from a given distribution are often called \"random variates\" or just \"variates\" for short; to \n", "generate size random variates from a normal distribution with mean loc and standard \n", "deviation scale we can use the scipy.stats function \n", "
\n",
    " X = norm.rvs(loc=0,scale=1,size=num_trials)\n",
    "
\n", "\n", "(Note that in this case, the normal is defined in terms of the standard devation, and not the variance.)\n", "\n", "Run the next cell several times to get a sense for how this function works" ] }, { "cell_type": "code", "execution_count": 53, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "From N(0,1):\n", "-2.4221520417392313\n", "\n", "From N(10,2^2):\n", "11.779694860358964\n", "\n", "Ten variates from N(66,3^2):\n", "[67.86317916 62.81627429 71.02267807 67.92493406 69.01923287 64.30318126\n", " 69.81129266 65.78251048 71.17414328 63.83041032]\n" ] } ], "source": [ "print(\"From N(0,1):\")\n", "X = norm.rvs() # default is a standard normal with mean 0 and standard deviation 1\n", "print(X)\n", "print()\n", "print(\"From N(10,2^2):\")\n", "X = norm.rvs(10,2) # defined by mean and standard deviation (NOT the variance)\n", "print(X)\n", "print()\n", "print(\"Ten variates from N(66,3^2):\")\n", "X = norm.rvs(66,3,size=10)\n", "print(X)\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Graphing Continuous Variates: A Problem\n", "So generating normal variates is easy! What we are going to concern ourselves with in this next problem is now to graph a collection of such normal numbers. \n", "\n", "Here is the problem: since each value occurs (with high probability) only once, we can't just create a histogram and convert it into a frequency distribution. \n", "\n", "Here is what happens if we do this, and graph it as a scatter plot against the theoretical (continuous) distribution:" ] }, { "cell_type": "code", "execution_count": 95, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def display_normal_samples(mu,sigma,num_trials):\n", " fig, ax = plt.subplots(1,1,figsize=(12,6))\n", " plt.title('Analytical and Experimental Distributions for N('+str(mu)+','+str(sigma)+')')\n", " plt.ylabel(\"P(X=k)\")\n", " plt.xlabel(\"k in Range(X)\")\n", " # use normal(...) to generate random samples\n", " X = sorted(norm.rvs(mu,sigma,num_trials))\n", " # Now conv0\n", "display_normal_samples(66,3,num_trials)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "\n", "\n", "\n", "### Graphing Continuous Variates with Bins\n", "You see the problem: since each floating point number (an approximation of a real number) is \n", " generated with high probability at most once, we can't see the accumulation of samples that would\n", " indicate the probability. \n", "Essentially we are trying to create a frequency distribution from values whose theoretical probability is 0. What to do? \n", "\n", " Well, you know that probabilities can only be calculated in continuous distributions using intervals, so we will create equally-sized intervals to collect together our samples from the continuous distribution. Then we must \"slot\" each variate into its appropriate bin and calculate the probabilities. \n", "\n", "Thus, we transform a continuous distribution into a discrete one for the purposes of visualizing it. \n", " \n", " \n", "The pyplot function hist(...) does the slotting, if we give it a list of outcomes and the bin boundaries, so\n", "that really all we have to do is define the bins. \n", "\n", "### Graphing Normal Variates with Bins Calculated from Standard Deviation\n", "\n", "For the normal distribution it makes sense to define the bin boundaries in terms of standard deviations from the mean, since we will be dealing with an unknown range of data; this bins can be made as wide or as narrow as we want, but will represent an interval defined in terms of the standard deviation sigma of the distribution. \n", "\n", "We will graph the distribution in a range of at least 4 standard deviations of the mean, ignoring the rare occurance of a variate outside this range. " ] }, { "cell_type": "code", "execution_count": 96, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "[-4.0, -3.75, -3.5, -3.25, -3.0, -2.75, -2.5, -2.25, -2.0, -1.75, -1.5, -1.25, -1.0, -0.75, -0.5, -0.25, 0.0, 0.25, 0.5, 0.75, 1.0, 1.25, 1.5, 1.75, 2.0, 2.25, 2.5, 2.75, 3.0, 3.25, 3.5, 3.75, 4.0]\n" ] } ], "source": [ "# Define the boundaries of bins with the specified width around the mean, \n", "# to plus/minus at least 4 * sigma\n", "\n", "# bin_width is in units of sigma, so bin_width = 0.1 means sigma/10\n", "\n", "def makeBins(mu,sigma,bin_width):\n", " numBins = ceil(4/bin_width)\n", " bins = [mu+sigma*bin_width*x for x in range(-numBins,numBins+1)]\n", " return bins\n", "\n", "# Change the parameters several times to see the effect of this\n", "\n", "print(makeBins(0,1,.25))\n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem Eight: Generating and Graphing Normal Variates\n", "\n", "### How does the number of trials affect the fit of the data to the normal distribution?\n", "Now let's do our previous experiment but trying various \n", "values for `bin_width`..." ] }, { "cell_type": "code", "execution_count": 117, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "def display_normal_samples_binned(mu,sigma,num_trials,bin_widths):\n", " fig, ax = plt.subplots(1,1,figsize=(12,6))\n", " plt.title('Analytical and Experimental Distributions for N('+str(mu)+','+str(sigma)+')')\n", " plt.ylabel(\"f(k)\")\n", " plt.xlabel(\"k in Range(X)\")\n", " # use norm.rvs(...) to generate random samples\n", " X = norm.rvs(mu,sigma,num_trials)\n", " plt.hist(X,bins=makeBins(mu,sigma,bin_widths),density=True,edgecolor='k',alpha=0.5) # bins are of width 1/10**decimals\n", " #plt.hist(X,bins=makeBins(mu,sigma,bin_widths),density=True,edgecolor='k',alpha=0.5) # use if get warning\n", " # Now generate the theoretical normal with the same mean and \n", " X2 = np.linspace(mu-sigma*3,mu+sigma*3,100)\n", " Y = [norm.pdf(x,mu,sigma) for x in X2]\n", " plt.plot(X2,Y)\n", " plt.show()\n", " \n", "#try each of these and observe the effects\n", "\n", "N = 1000000 # try 100, 1000, and 1,000,000\n", "\n", "display_normal_samples_binned(66,3,N,0.05) \n", " " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Clearly the data seems to fit the normal better when the number of trials increases...\n", "\n", "### Affect of the bin width\n", "\n", "But now let's think about the issue of precision, i.e., the width of the bins.\n", "Again, try each of the following and see what happens. You can see that too-wide bins don't give much information, but too-narrow bins don't show how the data fits the normal distribution. There is a relationship between the number of data points and the width of the bins." ] }, { "cell_type": "code", "execution_count": 123, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "bin_width = 0.1 # try changing this to 0.5, 0.2, 0.1, 0.05, and 0.01\n", "\n", "display_normal_samples_binned(66,3,1000,bin_width)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (A)\n", "Clearly the \"fit\" with the normal curve depends on the width of the bins!\n", "For the following three examples, find a value for the indicated parameter which gives a good correspondence\n", "between the normal curve and the data. " ] }, { "cell_type": "code", "execution_count": 153, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", "text/plain": [ "
" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Problem 1(a)\n", "bin_width = 0.1 # experiment with this value 0.01, 0.05, 0.1, 0.15, etc. -- find the \n", " # largest number which still gives a good fit\n", " \n", "display_normal_samples_binned(0,10,100000,bin_width) # don't change this line\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (B)" ] }, { "cell_type": "code", "execution_count": 130, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Problem 1(b)\n", "\n", "bin_width = 0.1 # experiment with this value -- find the largest number which still \n", " #. gives a good fit\n", "\n", "display_normal_samples_binned(0,0.1,10000,bin_width) # don't change this line\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (C)" ] }, { "cell_type": "code", "execution_count": 141, "metadata": {}, "outputs": [ { "data": { "image/png": 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\n", 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" ] }, "metadata": { "needs_background": "light" }, "output_type": "display_data" } ], "source": [ "# Problem 11(c)\n", "\n", "bin_width = 0.1 # experiment with this value -- find the largest number which still \n", " # gives a good fit\n", "\n", "display_normal_samples_binned(1000,100,10000,bin_width) # don't change this line\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Part (D)\n", "\n", "What do you think is a good value for `bin_width` in general, assuming that `num_trials` is \n", "sufficient to give a reasonable approximation of the normal distribution?\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "**Solution:** " ] } ], "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 }