Problem 2 (5 points): At a store, a customer buys a random amount X of fresh ground peanut butter that is exponentially distributed with mean weight 20 oz. The store offers a discount, where every oz up to 25 oz costs 40 cents and every additional oz beyond that costs 30 cents (eg. for 30 oz of peanut butter, the customer pays 25 -0.4+5-0.3 = 115$). (i) What is the probability that the customer buys more than 25 oz of peanut butter? (ii) Given that the customer buys more than 25 oz, what is the expected amount of peanut butter they buy? (iii) Express the price Y that the customer pays for the peanut butter as a function of X . Compute the expected price ]E(Y) that the customer pays