1. A company is trying to sell one of four products. They rank the probability that the customer will buy the product and the amount of money that the company will earn is as follows: 0.2 ifx = -$50, 0.3 ifx = $100, f(x) = 0.3 ifx = $200, A if x = $400, otherwise a. Find A. b. Find the moment generating function of this distribution. c. Find the characteristic function of X. d. Use the moment generating function to find the first 2 moments of X