An appliance dealer sells three different models of upright

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.

(a) Compute E(X), E(X²), and V(X). (Round your answers to two decimal places.)

E(X) = ??? ft^3
E(X2) = ??? ft^6
V(X) = ??? ft^6

(b) If the price of a freezer having capacity X cubic feet is 29X ? 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 29X ? 8.5 paid by the next customer? (Round your answer to the nearest whole number.)
dollars²

(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.)
ft³

13.5 15.9 19.1 p(x) 0.16 0.51 0.33

Solution

(a)

E(X) = 0.16*13.5 + 0.51*15.9 + 0.33*19.1 = 16.57

E(X²) = 0.16*13.5² + 0.51*15.9² + 0.33*19.1² =278.48

V(X) = E(X²)- [E(X)]² = 3.85

(b)

P = 29X - 8.5

E(P) = 29*E(X) - 8.5 = 29*16.572-8.5 = 472

(c)

V(P) = sqrt(29)V(X) = sqrt(29)*3.849216 = 21

(d)

h(X) = X-0.01X²

E(h(X)) = E(X)-0.01E(X²) = 16.572 - 0.01*278.4804 =13.787