We will use the Minitab macro NormGCP.mac to find the posterior distribution of the normal mean µ when we have a random samples of size n of normal

(µ, σ2) observations with known σ2 = 22, and we have a general continuous prior for µ. Suppose the prior has the shape given by g(µ) =







µ for 0 < µ ≤ 3 3 for 3 <µ< 5 8 − µ for 5 < µ ≤ 8 0 for 8 < µ

Store the values of µ and prior g(µ)in column c1 and c2, respectively. Suppose the random sample of size n = 16 is:4.09 4.6 1.87 2.62  5.58 8.68  4.07 4.78  4.79 4.49  5.85 5.90  2.40 6.27  6.30 4.47

(a) UseNormGCP.mac to determine the posterior distribution g(µ|y1,...,y16).

Details for invoking NormGCP.mac are in Appendix 3.

(b) Use tintegral.mac to find the posterior mean and posterior standard deviation of µ. Details for invoking tintegral.mac are in Appendix 3.

(c) Find a 95% credible interval for µ by using tintegral.mac.