1. The random variables X and Y have the following joint probability distribution (X values in the first row and )' values in the first column): YXO 1 2 1 0.2 0 0.2 2 0 0.2 0 3 0.2 0 0.2 (a) Find and plot the marginal distributions of X and Y', and their cumulative distribution functions. (c) Find their correlation coefficient. Are X and Y independent? (b) Find the mean and variance of and E(X|Y). (d) Find the numerical values of a and 3 in the regression line E(X Y) = a + BY. (e) Let Z = 2X - E(X Y) + Y. Find E(Z)