We are given two independent random variables, M and K

We are given two independent random variables. M and K, both taking integer values between O and Further. assume that you that the distribution of K is uniform; i.e., P (K i) 1/100 for all i {0, l, 2, , 99}. You do not know anything else about the distribution of M. Finally, eve define a new random variable C as C - (M + K) mod . a) For all fixed values m, c e (0, 1, , 99}. use what you know about modular arithmetic and the independence Of random variables M and K to write the probability p (C c, M Tn) in terms Of P (M m). b) Use part a) and the Law of Total Probability to compute p (C c) as a function of c e {O, 1, , c) Use the definition of independence together with your solutions to parts a) and b) to show that M and C are (mutually) independent.