The question is as the picture.

8. The random variables X and Y are independent and identically distributed (iid). The random variable X takes on values 8x = (x1, x2, x3,x4) - {-3.-1, 1, 3) with probabilities Px - {1/4.3/8,3/8, 1/4). The joint set is denoted as 8x - 8x x SY- (a.) Calculate the mean value #x = E[X], (b.) Calculate the variance of = E[(X - ux)-1. (c.) Write the set 8z in terms of the pair (x;, y;) where i, j = 1,2,3,4. For example 8z = ((x. "). (x. 52). (X1. 13). .... (X4. ))). (d.) Calculate the probabilities Pz. (e.) If a new random variable R - X? + Y?, determine the cdf FR(r)