31. 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 pmf x 13.5 15.9 19.1 p(x) .2 .5 .3

a. Compute E(X), E(X2), and V(X).

b. If the price of a freezer having capacity X cubic feet is 25X  8.5, what is the expected price paid by the next customer to buy a freezer?

c. What is the variance of the price 25X  8.5 paid by the next customer?

d. Suppose that although the rated capacity of a freezer is X, the actual capacity is h(X)  X 

.01X2. What is the expected actual capacity of the freezer purchased by the next customer?