Suppose that a random sample of sizen is taken from a Poisson distribution for which the value of the mean e is unknown, and the prior distribution of e is a gamma distribution for which the mean is Pg. Show that the mean of the posterior distribution of e will be a weighted average having the form YnX,+ (1 – Yn)Ho, and show that yn - 1 as n→ *.
Suppose that a random sample of sizen is taken from a Poisson distribution for which the value of the mean e is unknown, and the prior distribution of e is a gamma distribution for which the mean is Pg. Show that the mean of the posterior distribution of e will be a weighted average having the form YnX,+ (1 – Yn)Ho, and show that yn - 1 as n→ *.
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.CR: Chapter 13 Review
Problem 44CR
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