PLEASE Don't use answer!!

Consider the Bayesian linear model yi~ N(x;B, 0' ), 1=1,...,n, n n where ri =0, x =n and 1= 1 The prior for 8 and the dummy variable z is given by T(B|z) = (1 - =)do(B) + =N(B|0, 72) and n(2) = q'(1 -q)1-. Suppose o, T and q are all known and do(B) is the indicator function which is 1 when 8 = 0 and is 0 otherwise. So, 8 = 0 if z = 0 and B = N(0, 72) if = = 1. (1) (8 pts) Find p(y1, . . . . Un|= = 0). (2) (12 pts) By integrating out B, find p(y1, . . . , Un|= = 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(2 = 1/y1, ..., yn) takes this value when n - co