Suppose X1 and X2 are two random variables with a joint density fX1,X2 (s, t). Suppose that fX1,X2 (s, t) = fX1,X2 (t, s) for all s, t. Which of the following is true? Justify your answer completely.

(a)The two random variables X1 and X2 are independent.

(b)The conditional expectation E[X1|X1 + X2] is equal to the conditional expectation E[X2|X1 + X2].

(c)The random variable M = max{X1, X2} is independent of the indicator random variable Z = 1 when X1>X2.