Solution Found!
Let X1, X2, ... , Xn be a random sample from a gamma distribution with known and with =
Chapter 6, Problem 6.8-2(choose chapter or problem)
Let X1, X2, ... , Xn be a random sample from a gamma distribution with known and with = 1/ . Say has a prior pdf that is gamma with parameters 0 and 0, so that the prior mean is 00. (a) Find the posterior pdf of , given that X1 = x1, X2 = x2, ... , Xn = xn. (b) Find the mean of the posterior distribution found in part (a), and write it as a function of the sample mean X and 00. (c) Explain how you would find a 95% interval estimate of if n = 10, = 3, 0 = 10, and 0 = 2.
Questions & Answers
QUESTION:
Let X1, X2, ... , Xn be a random sample from a gamma distribution with known and with = 1/ . Say has a prior pdf that is gamma with parameters 0 and 0, so that the prior mean is 00. (a) Find the posterior pdf of , given that X1 = x1, X2 = x2, ... , Xn = xn. (b) Find the mean of the posterior distribution found in part (a), and write it as a function of the sample mean X and 00. (c) Explain how you would find a 95% interval estimate of if n = 10, = 3, 0 = 10, and 0 = 2.
ANSWER:Step 1 of 10
(a).
It is given that 
