Please state whether the following statements are true or false and provide justification.

(a) Let X and Y be random variables such that P(X > 0) = 1 and P(Y < 0) = 1, then E[XY] < 1.

(b) Let X and Y be random variables such that P(X > 0) = 1 and P(Y < 0) = 1, then X and Y are

always negatively correlated.

(c) X and Y must be uncorrelated if Cov(X², Y²) = 0.

(d) The maximum possible value of Cov(X, Y) is 8 if Var(X) = 10 and Var(Y) = 2.