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. X 16 18 20 0.5 0.3 0.2 p(x) (a) Compute E(X), E(X²), and V(X). E(X)= ft3 E(X²) = V(x) = (b) If the price of a freezer having capacity X is 60X- 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?

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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.
20
16 18
0.5 0.3 0.2
p(x)
(a) Compute E(X), E(X2), and V(X).
E(X) =
ft³
E(X2) = |
V(X) =
(b) If the price of a freezer having capacity X is 60X 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 -0.009x². What is the expected actual capacity of the freezer purchased by the next customer? (Enter your answer to four decimal places.)
ft3
Transcribed Image Text: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. 20 16 18 0.5 0.3 0.2 p(x) (a) Compute E(X), E(X2), and V(X). E(X) = ft³ E(X2) = | V(X) = (b) If the price of a freezer having capacity X is 60X 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 -0.009x². What is the expected actual capacity of the freezer purchased by the next customer? (Enter your answer to four decimal places.) ft3
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