A 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 pmf x 16 18 20 p(x) 0.2 0.5 0.3 a. Compute E(X), E(X2), and V(X). b. If the price of a freezer having capacity X is 70X - 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 - 0.008X2. What is the expected actual capacity of the freezer purchased by the next customer?

A First Course in Probability (10th Edition)
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A 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 pmf

x 16 18 20
p(x) 0.2 0.5 0.3


a. Compute E(X), E(X2), and V(X).


b. If the price of a freezer having capacity X is
70X - 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 - 0.008X2. What
is the expected actual capacity of the freezer purchased by the next customer?

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