The owner of a small newspaper kiosk orders copies of a Vogue magazine for its rack each week. Let X = weekly demand for the Vogue magazine with cumulative distribution function F(x) in table below. X 0 1 2 3 F(x) 0.20 0.45 0.90 1.0 A. Prove that P(x) given by f(x) is a probability mass function. (2 points) B. What is the probability of selling at most one magazine? (1 points) C. What is the probability of selling more than 0 and less than 3 magazines? (1 points) D. What is the expected value and variance of the number of magazines that will be sold in a week? (4 points) E. Assume that each magazine costs the owner $25, and the owner has a fixed cost of $40. If he orders 2 magazines at the beginning of a week, what is his expected cost? (2 points)