8. -/6 POINTS DEVORESTAT7 3.P.032. MY NOTES An appliance dealer sells three different models of upright freezers having 13.5, 15.9, and 19.1 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by the next customer to buy a freezer. Suppose that X has the following pmf. X 13.5 15.9 19.1 p(x) 0.16 0.57 0.27 (a) Compute E(X), E(X2), and V(X). (Round your answers to two decimal places.) E(X) = E(X2) = V(X) = (b) If the price of a freezer having capacity X cubic feet is 26X - 8.5, what is the expected price paid by the next customer to buy a freezer? (Round your answer to the nearest whole number.) (c) What is the variance of the price 26X - 8.5 paid by the next customer? (Round your answer to the nearest whole number.) (d) Suppose that although the rated capacity of a freezer is X, the actual capacity is h(X) = X - 0.01X2. What is the expected actual capacity of the freezer purchased by the next customer? (Round your answer to three decimal places.)