2. Let X be a Chi-squared random variable with density functionafx (x) =expx > 0.Suppose Y is independent of, and has the same distribution as, X.(a) Let Z = vX. Show that the density function of Z is given by%3Dfz(z) = 2a expz > 0.Hence state the value of a.(b) Let V = X +Y and W = X/Y. Show that the joint density of V and W isgiven by1fv,w(v, w) =v, w > 0.ev/22T /w(w +1)

Answered: Image /qna-images/answer/2c614b45-5a54-4c5d-a3a0-9f7c719916fd.jpg

Answered: 2. Let X be a Chi-squared random…

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.

Chapter13: Probability And Calculus

Section13.2: Expected Value And Variance Of Continuous Random Variables

Problem 23E

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