(15 Points) Let X be a random variable that takes on values {1, 2, 3, 4} with probabilities {1/2, 1/4, 1/8, 1/8}. Let Y be another random variable that is equal to X with probability p. Show that the mutual information between X and Y is bounded by: I(X;Y) > 2p - Hp) - 0.25 (bits) Hint: You can use Fano's inequality