We roll two four-sided dice, one blue, the other red. Each die individually has sample space = {1,2,3,4}, with equiprobable outcomes. Define X, to be the random variable whose value is the outcome of the red die, and X, the random variable whose value is the outcome of the blue die. (a) Define the random variable X = X + Xb, that is the sum of the two rolls. What values does X take, and what is its pmf px? (b) Compute E(X). (c) Compute var(X). (d) Now let B be the event corresponding to the red die rolls a number higher than the blue die'. What is P(B)? (e) What is the conditional expectation E(X,|B)? What is E(XB)? What is E(X|B)?