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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![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 Po. Show that the mean of the posterior distribution of e will be a weighted average
having the form Y,X, + (1– Yn)Ho, and show that yn →1 as n- *.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48af0b99-9daa-414e-9d95-69f77d059bec%2Fe978cecc-d0e5-488f-bb21-f2041bf5f8ea%2Fm72hu7b_processed.png&w=3840&q=75)
Transcribed Image Text: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 Po. Show that the mean of the posterior distribution of e will be a weighted average
having the form Y,X, + (1– Yn)Ho, and show that yn →1 as n- *.
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