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 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.

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

(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 0.008X2. What is the expected actual capacity of the freezer purchased by the next customer?

Explanation / Answer

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.

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

(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 0.008X2. What is the expected actual capacity of the freezer purchased by the next customer?

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