Let X be a discrete random variable with probability function ft?) :P(X 2.1:) : :r: for 3:: 11213,... ' (a) Find the cumulative distribution function of X. (b) Find P(X = 4 + .1: | X > 4),:5 = 1,21 and compare the value with P(X = :t'). (e) Let R be the remainder when X is divided by 4. Find the probability function and the cumulative distribution function for R. (cl) Find E(R) and Var(R)