1. (10) Let random variable X be uniformly distributed between L and U such that both L and U are positive and U > L. (a) Calculate Ent [X], the entropy of X. (2) (b) Calculate Ent[X2]. (2) (c) Calculate Ent[c, X] and Ent[c2 X2] where c1 and c2 are some real numbers. (2+2) (d) What should be the relation between c, and c2, such that Ent[c, X] = Ent[c2X2]. (2)