An Introduction to Mathematical Statistics and Its Applications (6th Edition)
6th Edition
ISBN: 9780134114217
Author: Richard J. Larsen, Morris L. Marx
Publisher: PEARSON
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Chapter 5 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 5.2 - A random sample of size...Ch. 5.2 - The number of red chips and white chips in an urn...Ch. 5.2 - Use the sample y1=8.2,y2=9.1,y3=10.6, and y4=4.9...Ch. 5.2 - Suppose a random sample of size n is drawn from...Ch. 5.2 - Given that y1=2.3,y2=1.9, and y3=4.6 is a random...Ch. 5.2 - Use the method of maximum likelihood to estimate ...Ch. 5.2 - An engineer is creating a project scheduling...Ch. 5.2 - The following data show the number of occupants in...Ch. 5.2 - For the Major League Baseball seasons from 1950...Ch. 5.2 - (a) Based on the random sample...
Ch. 5.2 - Find the maximum likelihood estimate for in the...Ch. 5.2 - A random sample of size n is taken from the pdf...Ch. 5.2 - If the random variable Y denotes an individuals...Ch. 5.2 - For the negative binomial pdf...Ch. 5.2 - The exponential pdf is a measure of lifetimes of...Ch. 5.2 - Suppose a random sample of size n is drawn from a...Ch. 5.2 - Let y1,y2,...,yn be a random sample of size n from...Ch. 5.2 - Prob. 18QCh. 5.2 - A criminologist is searching through FBI files to...Ch. 5.2 - Prob. 20QCh. 5.2 - Suppose that Y1=8.3,Y2=4.9,Y3=2.6, and Y4=6.5 is a...Ch. 5.2 - Find a formula for the method of moments estimate...Ch. 5.2 - Calculate the method of moments estimate for the...Ch. 5.2 - Find the method of moments estimates for and 2,...Ch. 5.2 - Use the method of moments to derive estimates for...Ch. 5.2 - Bird songs can be characterized by the number of...Ch. 5.2 - Prob. 27QCh. 5.3 - A commonly used IQ test is scaled to have a mean...Ch. 5.3 - The production of a nationally marketed detergent...Ch. 5.3 - Mercury pollution is widely recognized as a...Ch. 5.3 - A physician who has a group of thirty-eight female...Ch. 5.3 - Suppose a sample of size n is to be drawn from a...Ch. 5.3 - What confidence would be associated with each of...Ch. 5.3 - Five independent samples, each of size n, are to...Ch. 5.3 - Suppose that y1,y2,...,yn is a random sample of...Ch. 5.3 - If the standard deviation () associated with the...Ch. 5.3 - In 1927, the year he hit sixty home runs, Babe...Ch. 5.3 - A thirty-second commercial break during the...Ch. 5.3 - During one of the first beer wars in the early...Ch. 5.3 - The Pew Research Center did a survey of 2253...Ch. 5.3 - If (0.57,0.63) is a 50% confidence interval for p,...Ch. 5.3 - Suppose a coin is to be tossed n times for the...Ch. 5.3 - On the morning of November 9, 1994the day after...Ch. 5.3 - Which of the following two intervals has the...Ch. 5.3 - Prob. 18QCh. 5.3 - Prob. 19QCh. 5.3 - Prob. 20QCh. 5.3 - Prob. 21QCh. 5.3 - A public health official is planning for the...Ch. 5.3 - Prob. 23QCh. 5.3 - Given that a political poll shows that 52% of the...Ch. 5.3 - Prob. 25QCh. 5.3 - Suppose that p is to be estimated by Xn and we are...Ch. 5.3 - Let p denote the true proportion of college...Ch. 5.3 - Prob. 28QCh. 5.4 - Two chips are drawn without replacement from an...Ch. 5.4 - Suppose a random sample of size n=6 is drawn from...Ch. 5.4 - Prob. 3QCh. 5.4 - A sample of size n=16 is drawn from a normal...Ch. 5.4 - Suppose X1,X2,...,Xn is a random sample of size n...Ch. 5.4 - Prob. 6QCh. 5.4 - Let Y be the random variable described in Example...Ch. 5.4 - Suppose that 14, 10, 18, and 21 constitute a...Ch. 5.4 - A random sample of size 2, Y1 and Y2, is drawn...Ch. 5.4 - A sample of size 1 is drawn from the uniform pdf...Ch. 5.4 - Suppose that W is an unbiased estimator for . Can...Ch. 5.4 - We showed in Example 5.4.4 that 2=1ni=1n(YiY)2 is...Ch. 5.4 - As an alternative to imposing unbiasedness, an...Ch. 5.4 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.4 - An estimator n=h(W1,...,Wn) is said to be...Ch. 5.4 - Is the maximum likelihood estimator for 2 in a...Ch. 5.4 - Let X1,X2,...,Xn denote the outcomes of a series...Ch. 5.4 - Suppose that n=5 observations are taken from the...Ch. 5.4 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.4 - Given a random sample of size n from a Poisson...Ch. 5.4 - If Y1,Y2,...,Yn are random observations from a...Ch. 5.4 - Suppose that W1 is a random variable with mean ...Ch. 5.5 - Let Y1,Y2,...,Yn be a random sample from...Ch. 5.5 - Let X1,X2,...,Xn be a random sample of size n from...Ch. 5.5 - Suppose a random sample of size n is taken from a...Ch. 5.5 - Let Y1,Y2,...,Yn be a random sample from the...Ch. 5.5 - Prob. 5QCh. 5.5 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.5 - Prove the equivalence of the two forms given for...Ch. 5.6 - Let X1,X2,...,Xn be a random sample of size n from...Ch. 5.6 - Let X1,X2, and X3 be a set of three independent...Ch. 5.6 - If is sufficient for , show that any one-to-one...Ch. 5.6 - Show that 2=i=1nYi2 is sufficient for 2 if...Ch. 5.6 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.6 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.6 - Suppose a random sample of size n is drawn from...Ch. 5.6 - Suppose a random sample of size n is drawn from...Ch. 5.6 - Prob. 9QCh. 5.6 - Prob. 10QCh. 5.6 - Prob. 11QCh. 5.7 - How large a sample must be taken from a normal pdf...Ch. 5.7 - Let Y1,Y2,...,Yn be a random sample of size n from...Ch. 5.7 - Suppose Y1,Y2,...,Yn is a random sample from the...Ch. 5.7 - An estimator n is said to be squared-error...Ch. 5.7 - Suppose n=Ymax is to be used as an estimator for...Ch. 5.7 - Prob. 6QCh. 5.8 - Prob. 1QCh. 5.8 - Find the squared-error loss [L(,)=()2] Bayes...Ch. 5.8 - Prob. 3QCh. 5.8 - Prob. 4QCh. 5.8 - Prob. 5QCh. 5.8 - Suppose that Y is a gamma random variable with...Ch. 5.8 - Prob. 7QCh. 5.8 - Find the squared-error loss Bayes estimate for in...Ch. 5.8 - Prob. 9Q
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- F Make a box plot from the five-number summary: 100, 105, 120, 135, 140. harrow_forward14 Is the standard deviation affected by skewed data? If so, how? foldarrow_forwardFrequency 15 Suppose that your friend believes his gambling partner plays with a loaded die (not fair). He shows you a graph of the outcomes of the games played with this die (see the following figure). Based on this graph, do you agree with this person? Why or why not? 65 Single Die Outcomes: Graph 1 60 55 50 45 40 1 2 3 4 Outcome 55 6arrow_forward
- lie y H 16 The first month's telephone bills for new customers of a certain phone company are shown in the following figure. The histogram showing the bills is misleading, however. Explain why, and suggest a solution. Frequency 140 120 100 80 60 40 20 0 0 20 40 60 80 Telephone Bill ($) 100 120arrow_forward25 ptical rule applies because t Does the empirical rule apply to the data set shown in the following figure? Explain. 2 6 5 Frequency 3 сл 2 1 0 2 4 6 8 00arrow_forward24 Line graphs typically connect the dots that represent the data values over time. If the time increments between the dots are large, explain why the line graph can be somewhat misleading.arrow_forward
- 17 Make a box plot from the five-number summary: 3, 4, 7, 16, 17. 992) waarrow_forward12 10 - 8 6 4 29 0 Interpret the shape, center and spread of the following box plot. brill smo slob.nl bagharrow_forwardSuppose that a driver's test has a mean score of 7 (out of 10 points) and standard deviation 0.5. a. Explain why you can reasonably assume that the data set of the test scores is mound-shaped. b. For the drivers taking this particular test, where should 68 percent of them score? c. Where should 95 percent of them score? d. Where should 99.7 percent of them score? Sarrow_forward
- 13 Can the mean of a data set be higher than most of the values in the set? If so, how? Can the median of a set be higher than most of the values? If so, how? srit to estaarrow_forwardA random variable X takes values 0 and 1 with probabilities q and p, respectively, with q+p=1. find the moment generating function of X and show that all the moments about the origin equal p. (Note- Please include as much detailed solution/steps in the solution to understand, Thank you!)arrow_forward1 (Expected Shortfall) Suppose the price of an asset Pt follows a normal random walk, i.e., Pt = Po+r₁ + ... + rt with r₁, r2,... being IID N(μ, o²). Po+r1+. ⚫ Suppose the VaR of rt is VaRq(rt) at level q, find the VaR of the price in T days, i.e., VaRq(Pt – Pt–T). - • If ESq(rt) = A, find ES₁(Pt – Pt–T).arrow_forward
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