Suppose that Y1 has a gamma distribution with parameters aj and ß, that Y¡ is gamma distributedwith parameters az and ß, and that Y1 and Y2 are independent. Let U1 = Y¡/(Y1+ Y2) and U2= Y1+Y2.a Derive the joint density function for U1 and U2.b Show that the marginal distribution of Uj is a beta distribution with parameters ɑj and a2.c Show that the marginal distribution of U2 is a gamma distribution with parameters a = aj+d2 and ß.d Establish that U1 and U2 are independent.

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Answered: Derive the joint density function for…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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Derive the joint density function for U1 and U2. Show that the marginal distribution of Uj is a beta distribution with parameters aj and a2. Show that the marginal distribution of Uz is a gamma distribution with parameters a = aj +a2 and ß. Establish that Uj and U2 are independent.