An certain brand of upright freezer is available in three different rated capacities: 16 ft?, 18 ft), and 20 ft?. Let X = the rated capacity of a freezer of this brand sold at a certain store. Suppose that X has the following pmf. x 16 18 20 P(x) | 0.3 0.4 0.3 (a) Compute E(X), E(X2), and V(X). E(X) = E(X2) = V(X) = ft3 (b) If the price of a freezer having capacity X is 62X – 650, what is the expected price paid by the next customer to buy a freezer? (c) What is the variance of the price paid by the next customer? (d) Suppose that although the rated capacity of a freezer is X, the actual capacity is h(X) = X – 0.009x2. What is the expected actual capacity of the freezer purchased by the next customer?