Problem 2 Consider the Bayesian linear model yi ~ N(xiB, 02), i = 1, ..., n, n n n where Exi = 0, Ex =n and Ciyi = Y. i=1 i=1 i-1 The prior for S and the dummy variable z is given by T(B|z) = (1 - z)do(B) + zN(310, 72) and 7(2) = q"(1 -q)1-z. Suppose o, T and q are all known and do(B) is the indicator function which is 1 when 3 = 0 and is 0 otherwise. So, B = 0 if z = 0 and B = N(0, 72) if z = 1. (3) (12 pts) Hence, find P(z = 1/y1, . .., yn). (4) (8 pts) What is P(z = 1/y1, ..., Un) when y = 0 and with large n? (5) (10 pts) Under the condition in (4), give an intuitive explanation why P(z = 1/y1, ..., yn) takes this value when n - co