Consider the simple linear regression model yi = ax + B(x; - x) +eu i = 1,...,n, where the errors e1, ..., en are independent with common distribution normal(0, o2) and o2 = 1 is known. The data are given in the table below. Xi Vi 1.1 N 3.1 2.8 3.9 U 6 Suppose that ax and B have independent normal priors given by ax ~normal (max, Sax) and B~normal(mg, SB), where max = 0, Sax = 1, mg = 0, SB = 1. a) Calculate and state the posterior distributions of ax and B. b) Test the null hypothesis Ho: B 2 0.95 versus H1 : B