Consider the Bayesian linear model where The prior for is given by Yi ~ N(xi, 0), 72 n =0, = n i=1 i= 1, ... ,n, i=1 and 72 riyi = Y. i=1 T(B) = 0.5 1(3 = 0) +0.5 N(3|0, 7), where 1(3 = 0) is the probability mass function which puts all probability on 3 = 0. Suppose and 7 are known. (3) (12 pts) Hence, show that T(BY, , Yn) x ..... and find vand . 7L IN(y | 0,0) 1(3 = 0) + m(y,..., Yn) N (B | v, ) (02)} z=1 (4) (8 pts) Hence, write down (3 = 0 | y,..., yn). (5) (10 pts) What is the significance of the term m(y, ..., yn) II1N(yi | 0,0) and show that this converges to infinity as y grows.