Answered: Let X, Y be independent random…

Let X, Y be independent random variables with exponential distribution of parameter θ > 0. Are the random variables Z = X + Y and W = X / (X+Y) independent?

Calculus For The Life Sciences

2nd Edition

ISBN:9780321964038

Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.

Chapter12: Probability

Section12.4: Discrete Random Variables; Applications To Decision Making

Problem 15E

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Question

Let X, Y be independent random variables with exponential distribution of parameter θ > 0. Are the random variables Z = X + Y and W = X / (X+Y) independent? (Prove using their respective graphs.)

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