Consider two investments, where investment i, i = 1, 2, costs Ci and yields the return Xi after 1 year, where X1 and X2 are random variables. Suppose C1 > C2. Are the following statements necessarily true?

(a) If E[X1] < E[X2], then there is an arbitrage.

(b) If P{X2 > X1} > 0, then there is an arbitrage.