Probability and Statistical Inference (9th Edition)
Probability and Statistical Inference (9th Edition)
9th Edition
ISBN: 9780321923271
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
Publisher: PEARSON
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Chapter 4.1, Problem 3E

Let the joint pmf of X and Y be defined by f ( x , y ) = x + y 32 , x = 1 , 2 , y = 1 , 2 , 3 , 4.

(a) Find f X ( x ) , the marginal pmf of X.

(b) Find f Y ( x ) , the marginal pmf of Y.

(c) Find P ( X   >   Y ) .

(d) Find P ( Y   =   2 X ) .

(c) Find P ( X + Y = 3 ) .

(f) Find P ( X 3 Y ) .

(g) Are X and Y independent or dependent? Why or why not?

(h) Find the means and the variances of X and Y.

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Chapter 4 Solutions

Probability and Statistical Inference (9th Edition)

Ch. 4.2 - Prob. 2ECh. 4.2 - Roll a fair four-sided die twice. Let X equal the...Ch. 4.2 - Let X and Y have a trinomial distribution with...Ch. 4.2 - Prob. 5ECh. 4.2 - The joint pmf of X and Y is f(x,y)=16,0x+y2, where...Ch. 4.2 - Let the joint pmf of X and Y be...Ch. 4.2 - A certain raw material is classified as to...Ch. 4.2 - Prob. 9ECh. 4.2 - If the correlation coefficient exists, show that...Ch. 4.3 - Let X and Y have the joint pmf...Ch. 4.3 - Let the joint pmf f(x,y) of X and Y be given by...Ch. 4.3 - Let W equal the weight of laundry soap in a...Ch. 4.3 - The gene for eye color in a certain male fruit fly...Ch. 4.3 - Let X and Y have a trinomial distribution with...Ch. 4.3 - An insurance company sells both homeowners...Ch. 4.3 - Using the joint pmf from Exercise 4.2-3, find the...Ch. 4.3 - A fair six-sided die is rolled 30 independent...Ch. 4.3 - Let X and Y have a uniform distribution on the set...Ch. 4.3 - Let fX(x)=110,x=0,1,2,...,9, and...Ch. 4.3 - Suppose that X has a geometric distribution with...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Show that the expression in the exponent of...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Let X and Y have a bivariate normal...Ch. 4.5 - Let X denote the height in centimeters and Y the...Ch. 4.5 - For a freshman taking introductory statistics and...Ch. 4.5 - For a pair of gallinules, let X equal the weight...Ch. 4.5 - Let X and Y have a bivariate normal distribution...Ch. 4.5 - Let X and Y have a bivariate normal distribution....Ch. 4.5 - In a college health fitness program, let X denote...Ch. 4.5 - For a female freshman in a health fitness program,...Ch. 4.5 - Prob. 12ECh. 4.5 - An obstetrician does ultrasound examinations on...
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