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.]
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 10E
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