1 and X2 be independent chi-squared random variables with r1 and r2 degrees of freedom, respectively. Show that, (a) U = X1/(X1+X2) has a beta distribution with alpha = r1/2 and beta = r2/2. (b) V = X2/(X1+X2) has a beta distribution with alpha = r2/2 and bet

1 and X2 be independent chi-squared random variables with r1 and r2 degrees of freedom, respectively. Show that, (a) U = X1/(X1+X2) has a beta distribution with alpha = r1/2 and beta = r2/2. (b) V = X2/(X1+X2) has a beta distribution with alpha = r2/2 and bet

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

Let X1 and X2 be independent chi-squared random variables with r1 and r2 degrees of freedom, respectively. Show that,

(a) U = X1/(X1+X2) has a beta distribution with alpha = r1/2 and beta = r2/2.

(b) V = X2/(X1+X2) has a beta distribution with alpha = r2/2 and beta = r1/2

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