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 4.3, Problem 1E

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

(a) Display the joint prnf and the marginal pmfs on a graph like Figure 4.3-1(a).

(b) Find g ( x | y ) and draw a figure like Figure 4.3-1(b), depicting the conditional pmfs for y = 1 , 2 , 3 , and 4.

(c) Find h ( y | x ) and draw a figure like Figure 4.3-1(c), depicting the conditional pmfs for x   =   1 and 2.

(d) Find P ( 1 Y 3 | X = 1 ) ,   P ( Y 2 | X = 2 ) , and P ( X   = 2 | Y = 3 ) .

(c) Find E ( Y | X =   1 ) and V a r ( Y | X =   1 ) .

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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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