2. Suppose X is a Poisson random variable with rate parameter A, where A is a randomvariable itself following a gamma prior distribution with known parameters a and ß.(a) Show that the posterior distribution of A given X = 1 is also a gamma distribu-tion, but with paramaters a + z andB+1'[Note: we have now shown that the gamma distribution is the conjugate prior forthe Poisson distribution.](b) Show that the Bayesian estimator, given by the mean of the posterior distributionfor A, isÂ = B(a + 1)B+1

Suppose X is a Poisson random variable with rate parameter A, where A is a random variable itself following a gamma prior distribution with known parameters a and ß. (a) Show that the posterior distribution of A given X = z is also a gamma distribu- tion, but with paramaters a +z and 3+1 [Note: we have now shown that the gamma distribution is the conjugate prior for the Poisson distribution.]

Suppose X is a Poisson random variable with rate parameter A, where A is a random variable itself following a gamma prior distribution with known parameters a and ß. (a) Show that the posterior distribution of A given X = z is also a gamma distribu- tion, but with paramaters a +z and 3+1 [Note: we have now shown that the gamma distribution is the conjugate prior for the Poisson distribution.]

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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