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9 Let X and Y be two continuous random variables with the joint proba- bility density f(x, y) = xe-x(+1) for x, y > 0 and f(x, y) = : 0 otherwise. What are the conditional density functions fx (x | y) and fy(y | x)? What is POY 11X= 1)2

9 Let X and Y be two continuous random variables with the joint proba- bility density f(x, y) = xe-x(+1) for x, y > 0 and f(x, y) = : 0 otherwise. What are the conditional density functions fx (x | y) and fy(y | x)? What is POY 11X= 1)2

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Question 7.9

268 7 Conditioning by Random Variables 7.9 Let X and Y be two continuous random variables with the joint proba- bility density f(x, y) = xe-xy+¹) for x, y > 0 and f(x, y) 0 and f(x, y) = 0 otherwise. What are the conditional density functions fx (x | y) and fy(y | x)? What is P(Y> 1 | X = 1)? Problems 7.10 Let X and Y be two continuous random variables with the joint probabil- ity density f(x, y) = x-y+1 for 0 < x, y < 1 and f(x, y) = 0 otherwise. What are the conditional densities fy(y | x) and fx(x | y)? What are P(X> 0.5 | Y = 0.25) and P(Y> 0.5 | X = 0.25)? 7.11 Let X and Y be two continuous random variables with the joint probabil- for 0 ≤ y ≤ x < 1 and f(x, y) ity density f(x, y) otherwise. = x -
Transcribed Image Text:268 7 Conditioning by Random Variables 7.9 Let X and Y be two continuous random variables with the joint proba- bility density f(x, y) = xe-xy+¹) for x, y > 0 and f(x, y) 0 and f(x, y) = 0 otherwise. What are the conditional density functions fx (x | y) and fy(y | x)? What is P(Y> 1 | X = 1)? Problems 7.10 Let X and Y be two continuous random variables with the joint probabil- ity density f(x, y) = x-y+1 for 0 < x, y < 1 and f(x, y) = 0 otherwise. What are the conditional densities fy(y | x) and fx(x | y)? What are P(X> 0.5 | Y = 0.25) and P(Y> 0.5 | X = 0.25)? 7.11 Let X and Y be two continuous random variables with the joint probabil- for 0 ≤ y ≤ x < 1 and f(x, y) ity density f(x, y) otherwise. = x -
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