Problem 3. (Updating prior distributions) Suppose X1, . .. , An are independent and identically distributed random variables with a Bernoulli () distribution, where / is itself a random variable with the following discrete prior distribution: P( = 1/4) = 1/3, P(1 = 2/3) = 1/2, P(1 = 7/8) =1/6 (a) Determine an expression for the posterior distribution P(ulXI, . . . , Xn) (b) Let X1 = 0, X2 = 1, X3 = 0, X1 = 0. Calculate P(u(X1 = 0, X2 = 1, X3 = 0, X1 = 0). (c) Suppose that X1 through X, are given as above. Compute P(ulX1, X2) Consider this to be the updated distribution of /, which we will denote pa-2(/); using this distribution now as the prior distribution of /, compute P(ulX3, XA) Does this answer coincide with the answer in part (b)