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) 0.20 0.59 0.21
(a) Compute E(X), E(X2), and V(X). (Round your answers to two decimal places.)
E(X) = ft3
E(X2) = ft6
V(X) = ft6
(b) If the price of a freezer having capacity X cubic feet is 22X + 8.5, what is the expected price paid by the next customer to buy a freezer? (Round your answer to the nearest whole number.)
dollars
(c) What is the variance of the price 22X + 8.5 paid by the next customer? (Round your answer to the nearest whole number.)
dollars
(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.)