Please help me with questions a, b, and c. Really appreciate it if you can solve these with a proper explanation (With full justification). So that I can understand how to do them. Thank you.

Please note all entropies and logarithms are to BASE 2

1. Consider the following two probability distributions: 1/4 if X = 0 Prob(X - j) = 3/4 if X = 1 and 3/8 if Y = 0 Prob(Y = j) = 5/8 if Y = 1 (a) Without further computation, state and justify if the following statement is true or false: H(X ) > H( Y). (b) Let Z = X +Y (mod 2), and assume that X and Y are independent. Calculate the probability distribution of Z. Without further computation, state and justify the ordering, from small to large, of the following three entropies: H(X), H(Y), H(Z). (c) (i) Calculate H(X|Z) = Zi=. Prob(Z = i) H(X|Z = i) and H(Z|X). (ii) From these quantities state if estimating Z given the value of X or estimating A given the value of Z is harder. Fully justify your answer (iii) Calculate the probability of error if you make the best estimate possible for the value of Z given that X = 0