For each of the following, say whether the assertion is true or false. If it is true, provide justification, and if it is false, give a counterexample. (a) For any finite sample space ? and any event A CQ, Pr( A) = A (b) If Y = X + Z is Gaussian, then X and Z are both marginally Gaussian. (c) Michael and Kevin are playing a game where Michael scores X, ~ Geometric(1/m) points and Kevin scores Y, ~ Geometric(1/k) points at round , independently of other rounds. Then, as the number of rounds goes to infinity, the average total number of points they score per round converges almost surely to m + k. (d) Suppose a random variable X is bounded in [0, 1], and furthermore suppose that E[X] > E. Then Pr(X > 2) > 2