An appliance dealer sells three different models of upright freezers having 13.5

Question

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) 0.16 0.60 0.24 (a) Compute Ex), E(x2), and Vx) E(X) E(X2)- (b) If the price of a freezer having capacity X cubic feet is 30x - 8.5, what is the expected price paid by the next customer to buy a freezer? (c) What is the variance of the price 30x -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 - 0.02x2. What is the expected actual capacity of the freezer purchased by the next customer?

Explanation / Answer

A) E(X) = 13.5 * 0.16 + 15.9 * 0.6 + 19.1 * 0.24 = 16.284

E(X2) = 13.52 * 0.16 + 15.92 * 0.6 + 19.12 * 0.24 = 268.4004

Var(X) = E(X2) - (E(X))2 = 268.4004 - 16.2842 = 3.2317

B) E(30 X - 8.5) = 30 * E(X) - 8.5 = 30 * 16.284 - 8.5 = 480.02

C) Var(30X - 8.5) = 302 * Var(X) = 900 * 3.2317 = 2908.53

D) E(X - 0.02X2) = E(X) - 0.02 * E(X2) = 16.284 - 0.02 * 268.4004 = 10.916

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