Let X be a discrete random variable with probability function f(x) = P(X = x) = 2 for x = 1, 2, 3, ... . (a) Find the cumulative distribution function of X. (b) Find P(X = 4 + x | X > 4), x = 1, 2, .... and compare the value with P(X = ). (c) Let R be the remainder when X is divided by 4. Find the probability function and the cumulative distribution function for R. (d) Find E(R) and Var(R)