1. Let X1, ...,Xl be mud from Now?) with 02 = 16 given and 2:21 a = 128. (a) Use a Bayes Test to test Ho : ,u = 7 vs H1 : ,u = 9 if Q = {pi} consists of only these 2 points with prior probabilities: \"(1\" = 7) = :2 and \"( = 9) = :1. (b) Suppose pi can be any real value with a prior distribution arm) = N06, 4). (i) Find the Bayes Estimate of pi. (ii) Find the 95% Highest Posterior Density (HPD) credible interval for a. (iii) Use a Bayes Test to test Ho : p, S 9 vs H1: pi > 9