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 9.4, Problem 6Q
Suppose
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1. Show, by using characteristic, or moment generating functions, that if
fx(x) = ½ex, -∞0 < x < ∞,
then XY₁ - Y2, where Y₁ and Y2 are independent, exponentially distributed
random variables.
1. Show, by using characteristic, or moment generating functions, that if
1
fx(x):
x) = ½ex
1990) 02-02
50% mesob
berceus
+7
What's the probability of getting more than
1 head on 10 flips of a fair coin?
Chapter 9 Solutions
An Introduction to Mathematical Statistics and Its Applications (6th Edition)
Ch. 9.2 - Some states that operate a lottery believe that...Ch. 9.2 - As the United States has struggled with the...Ch. 9.2 - Amedical researcher believes that women typically...Ch. 9.2 - Among a number of beliefs concerning the so-called...Ch. 9.2 - The University of MissouriSt. Louis gave a...Ch. 9.2 - Prob. 6QCh. 9.2 - Poverty Point is the name given to a number of...Ch. 9.2 - A major source of mercury poisoning comes from the...Ch. 9.2 - Despite its complexity, the English language does...Ch. 9.2 - A company markets two br ands of latex...
Ch. 9.2 - Prob. 11QCh. 9.2 - Suppose that H0:X=Y is being tested against H1:XY,...Ch. 9.2 - An executive has two routes that she can take to...Ch. 9.2 - Prob. 14QCh. 9.2 - If X1,X2,...,Xn and Y1,Y2,...,Ym are independent...Ch. 9.2 - Let X1,X2,...,Xn and Y1,Y2,...,Ym be independent...Ch. 9.2 - A person exposed to an infectious agent, either by...Ch. 9.2 - For the approximate two-sample t test described in...Ch. 9.2 - Prob. 19QCh. 9.2 - Two popular forms of mortgage are the thirty-year...Ch. 9.3 - Case Study 9.2.3 was offered as an example of...Ch. 9.3 - Question 9.2.20 compared the rates of thirty-year...Ch. 9.3 - Among the standard personality inventories used by...Ch. 9.3 - In a study designed to investigate the effects of...Ch. 9.3 - Raynauds syndrome is characterized by the sudden...Ch. 9.3 - The bitter, eight-month baseball strike that ended...Ch. 9.3 - For the data in Question 9.2.8, the sample...Ch. 9.3 - Crosstown busing to compensate for de facto...Ch. 9.3 - Show that the generalized likelihood ratio for...Ch. 9.3 - Let X0,X2,...,Xn and Y1,Y2,...,Ym be independent...Ch. 9.4 - The phenomenon of handedness has been extensively...Ch. 9.4 - In a study designed to see whether a controlled...Ch. 9.4 - Water witching, the practice of using the...Ch. 9.4 - If flying saucers are a genuine phenomenon, it...Ch. 9.4 - In some criminal cases, the judge and the...Ch. 9.4 - Suppose H0:pX=pY is being tested against H1:pXpY...Ch. 9.4 - A total of 8605 students are enrolled full-time at...Ch. 9.4 - Prob. 8QCh. 9.4 - Prob. 9QCh. 9.4 - Compute 2ln(see Equation 9.4.1) for the nightmare...Ch. 9.5 - Historically, fluctuations in the amount of rare...Ch. 9.5 - Male fiddler crabs solicit attention from the...Ch. 9.5 - Construct two 99% confidence intervals for XY...Ch. 9.5 - Prob. 4QCh. 9.5 - Prob. 5QCh. 9.5 - Construct a 95% confidence interval for X2/Y2...Ch. 9.5 - One of the parameters used in evaluating...Ch. 9.5 - Prob. 8QCh. 9.5 - Flonase is a nasal spray for diminishing nasal...Ch. 9.5 - Construct an 80% confidence interval for the...Ch. 9.5 - Prob. 11QCh. 9.5 - For obese patients, there is an increased risk of...
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- 9. The concentration function of a random variable X is defined as Qx(h) sup P(x≤x≤x+h), h>0. = x (a) Show that Qx+b(h) = Qx(h).arrow_forwardSuppose that you buy a lottery ticket, and you have to pick six numbers from 1 through 50 (repetitions allowed). Which combination is more likely to win: 13, 48, 17, 22, 6, 39 or 1, 2, 3, 4, 5, 6? barrow_forward2 Make a histogram from this data set of test scores: 72, 79, 81, 80, 63, 62, 89, 99, 50, 78, 87, 97, 55, 69, 97, 87, 88, 99, 76, 78, 65, 77, 88, 90, and 81. Would a pie chart be appropriate for this data? ganizing Quantitative Data: Charts and Graphs 45arrow_forward
- 10 Meteorologists use computer models to predict when and where a hurricane will hit shore. Suppose they predict that hurricane Stat has a 20 percent chance of hitting the East Coast. a. On what info are the meteorologists basing this prediction? b. Why is this prediction harder to make than your chance of getting a head on your next coin toss? U anoiaarrow_forward6. Show that one cannot find independent, identically distributed random variables X and Y such that X-YE U(-1, 1). 7 Consider al onarrow_forward2 Which situation is more likely to produce exactly 50 percent heads: flipping a coin 10 times or flipping a coin 10,000 times?arrow_forward
- 2. Let X1, X2..... X, be independent random variables with expectation 0 and finite third moments. Show, with the aid of characteristic functions, that E(X₁ + X₂++X)³ = EX² + EX²++ EX₁₂-arrow_forward21 Check out the sales of a particular car across the United States over a 60-day period in the following figure. 800- 700- 600- Number of items sold 400 500- Line Graph of Sales 3001 16 12 18 24 30 36 42 48 54 60 60 Day a. Can you see a pattern to the sales of this car across this time period? b. What are the highest and lowest numbers of sales, and when did they occur? c. Can Can you estimate the average of all sales over this time period?arrow_forward11 Bob has glued himself to a certain slot machine for four hours in a row now with his bucket of coins and a bad attitude. He doesn't want to leave because he feels the longer he plays, the better chance he has t win eventually. Is poor Bob right?arrow_forward
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