1. The transition matrix if given by - P P O C (a.) Assuming the output probability vector is 1 - p O p() |x) = P 0 0 - q q p(y) = p(y(x) p(x), - q calculate the mutual information / (X; Y), Assume the input/output alphabet is X = y = (a, b,c,d }, (b.) Determine the values of a, B, y, and & that maximizes the mutual information. and the input probability is