Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
10th Edition
ISBN: 9780137538461
Author: Robert Hogg, Elliot Tanis
Publisher: PEARSON+
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Textbook Question
Chapter 5.4, Problem 10E
Let X equal the outcome when a fair four-sided die that has its faces numbered 0, 1, 2, and 3 is rolled. Let Y equal the outcome when a fair four-sided die that has its faces numbered 0,4, 8, and 12 is rolled.
(a) Define the mgf of X.
(b) Define the mgf of Y.
(c) Let
(d) (live the pmf of W; that is. determine
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Chapter 5 Solutions
Pearson eText for Probability and Statistical Inference -- Instant Access (Pearson+)
Ch. 5.1 - Let X have a geometric distribution with parameter...Ch. 5.1 - Suppose that X is a continuous random variable...Ch. 5.1 - Prob. 3ECh. 5.1 - Prob. 4ECh. 5.1 - Let X have a gamma distribution with =3 and =2....Ch. 5.1 - The pdf of X is f(x)=2x,0x1. (a) Find the cdf of...Ch. 5.1 - Prob. 7ECh. 5.1 - Let X have a logistic distribution with pdf...Ch. 5.1 - A sum of $50000 is invested at a rate R, selected...Ch. 5.1 - The lifetime (in years) of a manufactured product...
Ch. 5.1 - Statisticians frequently use the extreme extreme...Ch. 5.1 - Prob. 12ECh. 5.1 - Let X have a Cauchy distribution. Find (a) P(X1)....Ch. 5.1 - Let f(x)=1[(1+x2)],x, be the pdf of the Cauchy...Ch. 5.1 - If X is N(,2), then M(t)=E(etX)=exp(t+2t22),t. We...Ch. 5.1 - Prob. 16ECh. 5.1 - Prob. 17ECh. 5.1 - (a) Let X be a continuous random variable with...Ch. 5.2 - Let X1,X2, denote two independent random...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Prob. 3ECh. 5.2 - Let the distribution of W be F(9, 24). Find the...Ch. 5.2 - Let the distribution of W be F(8. 4). Find the...Ch. 5.2 - Let X1 and X2 have independent gamma distributions...Ch. 5.2 - Let X1 and X2 be independent chi-square random...Ch. 5.2 - Let X have a beta distribution with parameters ...Ch. 5.2 - Determine the constant c such that...Ch. 5.2 - When and are integers and0p1, we have...Ch. 5.2 - Evaluate 00.4(7)(4)(3)y3(1y)2dy (a) Using...Ch. 5.2 - Let W1,W2 be independent, each with a Cauchy...Ch. 5.2 - Let X1, X2 be independent random variables...Ch. 5.2 - Prob. 14ECh. 5.2 - In Example 5.2-6, verify that the given...Ch. 5.2 - Show that if W has an F(r1,r2) distribution, then...Ch. 5.2 - Let W have an F distribution with parameters r1...Ch. 5.3 - Let X1 and X2 be independent Poisson random...Ch. 5.3 - Let X1 and X2 be independent random variables with...Ch. 5.3 - Let X1 and X2 be independent random variables with...Ch. 5.3 - Let X1 and X2 be a random sample of size n=2 from...Ch. 5.3 - Let X1 and X2 be observations of a random sample...Ch. 5.3 - Let X1 and X2 be a random sample of size n=2 from...Ch. 5.3 - The distributions of incomes in two Cities follow...Ch. 5.3 - Prob. 8ECh. 5.3 - Let X1,X2,...Xn be a random sample (of size n)...Ch. 5.3 - Let X1,X2,X3 denote a random sample of size n= 3...Ch. 5.3 - Let X1,X2,X3 be three independent random variables...Ch. 5.3 - Let X1,X2,X3 be a random sample of size n=3 from...Ch. 5.3 - Prob. 13ECh. 5.3 - Let X1,X2,X3 be independent random variables that...Ch. 5.3 - In considering medical insurance for a certain...Ch. 5.3 - The lifetime in months of a certain part has a...Ch. 5.3 - Two components operate in parallel in a device, so...Ch. 5.3 - Prob. 18ECh. 5.3 - Flip n=8 fair coins and remove all that came up...Ch. 5.3 - Prob. 20ECh. 5.4 - Let X1+X2+X3 be a random sample of size 3 from the...Ch. 5.4 - Let X1 and X2 have independent distributions...Ch. 5.4 - Prob. 3ECh. 5.4 - Generalize Exercise 5.4-3 by showing that the sum...Ch. 5.4 - Let Z1,Z2,....,Z7 be a random sample from the...Ch. 5.4 - Let X1,X2,X3,X4,X5 be a random sample of size 5...Ch. 5.4 - Let X1,X2,X3 denote a random sample of size 3 from...Ch. 5.4 - Let W=X1+X2+...+Xh, a sum of h mutually...Ch. 5.4 - Let X and Y, with respective pmfs f(x) and g(y),...Ch. 5.4 - Let X equal the outcome when a fair four-sided die...Ch. 5.4 - Let X and Y equal the outcomes when two fair...Ch. 5.4 - Let X and Y be the outcomes when a pair of fair...Ch. 5.4 - Let X1,X2,...,X8 be a random sample from a...Ch. 5.4 - The number of accidents in a period of one week...Ch. 5.4 - Given a fair four-sided die, let Y equal the...Ch. 5.4 - The number X of sick days taken during a year by...Ch. 5.4 - In a study concerning a new treatment of a certain...Ch. 5.4 - The number of cracks on a highway averages 0.5 per...Ch. 5.4 - A doorman at a hotel is trying to get three taxic...Ch. 5.4 - The time X in minutes of a visit to a...Ch. 5.4 - Let X and Y be independent with distributions...Ch. 5.4 - Let X1 and X2 be two independent random variables....Ch. 5.4 - Let X be N(0,1). Use the mgf technique to show...Ch. 5.4 - Let X1,X2,X3,X4 be a random sample from a x2(r)...Ch. 5.5 - Let X1,X2...,X16, be a random sample from a normal...Ch. 5.5 - Let X be N(50,36). Using the same set of axes,...Ch. 5.5 - Let X equal the widest diameter (in millimeters)...Ch. 5.5 - Let X equal the weight of the soap in a 6-pound...Ch. 5.5 - Let X equal the weight (in grams) of a nail of the...Ch. 5.5 - Let X1,X2,...,X100 be a random sample from N(,4),...Ch. 5.5 - Suppose that the distribution of the weight of a...Ch. 5.5 - Let X denote the wing length in millimeters of a...Ch. 5.5 - Suppose that the length of life in hours (say, X)...Ch. 5.5 - A consumer buys n light bulbs, each of which has a...Ch. 5.5 - A marketing research firm suggests to a comp any...Ch. 5.5 - Let the independent random variables X1 and X2 be...Ch. 5.5 - Prob. 13ECh. 5.5 - Let T have at distribution with r degrees of freed...Ch. 5.5 - Let the distribution of T be t(17). Find (a)...Ch. 5.5 - Prob. 16ECh. 5.6 - Let X be the mean of a random sample of size 12...Ch. 5.6 - Let Y=X1+X2+....+X15 be the sum of a random sample...Ch. 5.6 - Let X be the mean of a random sample of size 36...Ch. 5.6 - Approximate P(39.75X41.25), where X is the mean of...Ch. 5.6 - Let X1,X2,...,X18 be a random sample of size 18...Ch. 5.6 - A random sample of size ii = 18 is taken from the...Ch. 5.6 - Let X equal the maximal oxygen intake of a human...Ch. 5.6 - Let X equal the weight in grams of a miniature...Ch. 5.6 - In Example 5.6-4, with n=4, compute P(1.73.2) and...Ch. 5.6 - Prob. 10ECh. 5.6 - The tensile strength X of paper, in pounds per...Ch. 5.6 - At certain times during the year, a bus company...Ch. 5.6 - Prob. 13ECh. 5.6 - Suppose that the sick leave taken by the typical...Ch. 5.7 - Let the distribution of Y be b(25,1/2). Find the...Ch. 5.7 - Suppose that among gifted seventh-graders who...Ch. 5.7 - A public opinion poll in Southern California was...Ch. 5.7 - Let X equal the number out of n=48 mature aster...Ch. 5.7 - Let X1,X2,...,X48 be a random sample of size 48...Ch. 5.7 - In adults, the pneumococcus bacterium causes 70%...Ch. 5.7 - Let X equal the number of alpha particles emitted...Ch. 5.7 - A candy maker produces mints that have a label...Ch. 5.7 - Let X1,X2,...,X30 be a random sample of size 30...Ch. 5.7 - Prob. 10ECh. 5.7 - On January 1 of a given year, a college basketball...Ch. 5.7 - If X is b(100,0.1), find the approximate value of...Ch. 5.7 - Let X1,X2,...,X36 be a random sample of size 36...Ch. 5.7 - A die is rolled 24 independent times. Let V be the...Ch. 5.7 - In the United States, the probability that a child...Ch. 5.7 - Let X equal the sum of n=100 Bernoulli trials....Ch. 5.7 - The number of trees in one acre has a Poisson...Ch. 5.7 - Assume that the background noise X of a digital...Ch. 5.7 - A company has a one-year group life policy that...Ch. 5.8 - If X is a random variable with mean 33 and...Ch. 5.8 - If E(X)=17 and E(X2)=298, use Chebyshevs...Ch. 5.8 - Let X denote the outcome when a fair die is...Ch. 5.8 - If Y is b(n,0.5), give a lower bound for...Ch. 5.8 - If the distribution of Y is b(n,0.25), give a...Ch. 5.8 - Let X be the mean of a random sample of size n=15...Ch. 5.8 - Suppose that W is a continuous random variable...Ch. 5.9 - Let Y be the number of defectives in a box of 50...Ch. 5.9 - The probability that a certain type of inoculation...Ch. 5.9 - Let S2 be the sample variance of a random sample...Ch. 5.9 - Let Y be x2(n). Use the central limit theorem to...Ch. 5.9 - Let Y have a Poisson distribution with mean 3n....
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