Only need help with Part C (a) Let Z = vX. Show that the density function of Z is given byfz(z) = 2a exp2.z > 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 is%3Dgiven by1fv,w(v, w) =-0/2v, w > 0.2TVw(w+1)(c) Show that V and W are independent. State the distribution of V. 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.

For the joint pdf of V and W, we need to prove that random variables V and W are independent.

Answered: 1 fv,.w(v, w) = %3D 27Vw(w+1) e¯v/2 v,…

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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1 fv,.w(v, w) = %3D 27Vw(w+1) e¯v/2 v, w > 0. (c) Show that V and W are independent. State the distribution of V.