An certain brand of upright freezer is available in three different rated capacities: 16 ft³, 18 ft³, and 20 ft³. 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) | 0.1 0.2 0.7
(a) Compute E(X), E(X²), and V(X).
E(X) =
E(X²) =
V(X) =
(b) If the price of a freezer having capacity X is 63X - 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? (Enter your answer to four decimal places.)
