Solution Found!
Answer: Let X1,X2, . . . ,Xn be a random sample from a
Chapter 6, Problem 2E(choose chapter or problem)
Problem 2E
Let X1,X2, . . . ,Xn be a random sample from a gamma distribution with known α and with θ = 1/τ. Say τ has a prior pdf that is gamma with parameters α0 and θ0, so that the prior mean is α0θ0.
(a) Find the posterior pdf of τ , given that X1 = x1,X2 =x2, . . . ,Xn = xn.
(b) Find the mean of the posterior distribution found inpart (a), and write it as a function of the sample mean X and α0θ0.
(c) Explain how you would find a 95% interval estimate of τ if n = 10, α = 3, α0 = 10, and θ0 = 2.
Questions & Answers
QUESTION:
Problem 2E
Let X1,X2, . . . ,Xn be a random sample from a gamma distribution with known α and with θ = 1/τ. Say τ has a prior pdf that is gamma with parameters α0 and θ0, so that the prior mean is α0θ0.
(a) Find the posterior pdf of τ , given that X1 = x1,X2 =x2, . . . ,Xn = xn.
(b) Find the mean of the posterior distribution found inpart (a), and write it as a function of the sample mean X and α0θ0.
(c) Explain how you would find a 95% interval estimate of τ if n = 10, α = 3, α0 = 10, and θ0 = 2.
ANSWER:
Step 1 of 8
a) Given,
Conditional pdf of variable 
