I got x=1 = 1/2, x=2 = 5/12, x=3 = 1/2, but I'm not sure if im right.

Problem 8: Suppose that the moment generating function of the random variable X is Px (s) = 1+ 2es 1+ 3es 3 4 (a). What is the probability P(X = 1) ? (b). What is the probability P(X = 2) ? (c). What is the probability P(X = 3) ? Hint: Expand the product defining ox (s)