For each question, either explain why the statement is true or give a counterexample to the statement. You must explain your reasoning.

• a) Let (X, Y ) be jointly distributed random variables with joint pmf p(x, y), where p(x, y) = g(x) + h(y) for some functions g and h. Then X and Y are independent. (T/F?)
• b) If X is a random variable, then E[X²] E[X]. (T/F?)
• c) For events A and B if P( A | B ) = P(A) then A and B are independent. (T/F?)