(c) Show that the entropy of the probability distribution, (p1, . . . , Pi, . . . , Pm), is less than the entropy of the distribution (p], . .. . Piti ... Pitpi . . 2 . , Pm). (d) Let X be a random variable with m different outcomes X = {1, 2, . . . , m} and corresponding nonzero probabilities {91, 92, . . . ,9m} arranged in decreasing order. Now define a new random variable Y with m+1 different outcomes { 91 , 92 9m-1 9m 2}. Find the entropy of H(Y) in terms of H (X)