(a) Let X and Y be two independent continuous random variables. Prove Var(X + Y) = E(X2) + 50/2) [E(X)]2 [E(Y)]2. [2 points] (b) P is a probability measure. It is a function which assigns a number P(A) to each event A of the sample space S. Axiom 1: P(A) is real-valued with P(A) 2 0. Axiom 2: P(S) =1. Axiom 3: If two events A and B are mutually exclusive (A m B = 0): then P(A U B) = P(A) + P(B). Prove P(Z F) B) = P(B) P(A I\") B) based on the aforementioned axioms. [3 points]