2. Consider a stochastic process { Xo, X1, X2, X3} where each X; takes values in {+1, -1} and their joint distributions are given by 2 P(X, = 6;, 0 0 is some real number and Z is the normalizing constant which makes the above a probability measure. (a) Find P(X1 = 1/Xo = 1, X2 = 1, X3 = 1), P(X1 = 1/Xo = 1, X2 = 1, X3 = -1) and P(X1 = 1/Xo = 1, X2 = 1). (b) Find a general formula for P(X1 = 1|Xo = 60, X2 = 2) where 60, 62 E {+1, -1}. (c) For which value of go, 52 is the conditional expectation E(X1|Xo = 60, X2 = 2) maximum? (d) What happens to the probabilities in part (b) as Boo