An certain brand of upright freezer is available in three different rated capaci

Question

An certain brand of upright freezer is available in three different rated capacities: 16 ft, 18 , and 20 ft, Let X-the rated capacity of a freezer of this brand sold at a certain store suppose that X has the following pmf. 16 18 20 p(x) 0.4 0.50.1 (a) Compute E(X), E(X2), and V(X). E(X) = ft3 (b) If the price of a freezer having capacity X is 64X-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-0.008x?. what is the expected actual capacity of the freezer purchased by the next customer? ft3

Explanation / Answer

A) E(X) = 16 * 0.4 + 18 * 0.5 + 20 * 0.1 = 17.4

E(X2) = 162 * 0.4 + 182 * 0.5 + 202 * 0.1 = 304.4

V(X) = E(X2) - (E(X))2 = 304.4 - 17.42 = 1.64

B) E(64X - 650) = 64 * 17.4 - 650 = 463.6

C) V(64X - 650) = 642 * V(X) = 64 * 64 * 1.64 = 6717.44

D) E(X - 0.008X2) = E(X) - 0.008 * E(X2) =17.4 - 0.008 * 304.4 = 14.9648

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