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(Following Hogg, McKean & OCraig, exercise 11.2.2) Let X1, X2, ..., X10 be a random sample from a gamma distribution with a = 3 and ß = 1/0. Suppose we believe that e follows a gamma-distribution with a = 3 and B = 2: a) Find the posterior distribution of 0. b) If the observed x = 18.2, what is the Bayes point estimate associated with the square-error loss function? c) What is the Bayes point estimate using the mode of the posterior distribution? %3D

(Following Hogg, McKean & OCraig, exercise 11.2.2) Let X1, X2, ..., X10 be a random sample from a gamma distribution with a = 3 and ß = 1/0. Suppose we believe that e follows a gamma-distribution with a = 3 and B = 2: a) Find the posterior distribution of 0. b) If the observed x = 18.2, what is the Bayes point estimate associated with the square-error loss function? c) What is the Bayes point estimate using the mode of the posterior distribution? %3D

Calculus For The Life Sciences
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.
Chapter1: Functions
Section1.2: The Least Square Line
Problem 5E
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(Following Hogg, McKean & OCraig, exercise 11.2.2) Let X1, X2, ..., X10 be a random sample from a gamma distribution with a = 3 and ß = 1/0. Suppose we believe that e follows a gamma-distribution with a = 3 and B = 2: a) Find the posterior distribution of 0. b) If the observed x = 18.2, what is the Bayes point estimate associated with the square-error loss function? c) What is the Bayes point estimate using the mode of the posterior distribution? %3D
Transcribed Image Text:(Following Hogg, McKean & OCraig, exercise 11.2.2) Let X1, X2, ..., X10 be a random sample from a gamma distribution with a = 3 and ß = 1/0. Suppose we believe that e follows a gamma-distribution with a = 3 and B = 2: a) Find the posterior distribution of 0. b) If the observed x = 18.2, what is the Bayes point estimate associated with the square-error loss function? c) What is the Bayes point estimate using the mode of the posterior distribution? %3D
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