An certain brand of upright freezer is available in three different rated capacities: 16 ft³, 18 ft³, and 20 ft. Let X = the rated capacity of a freezer of thi a certain store. Suppose that X has the following pmf. 18 20 16 0.4 0.1 0.5 (a) Compute E(X), E(X²), and V(X). E(X)= E(X²) V(X)= X P(x) (b) If the price of a freezer having capacity X is 69X-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.
X
p(x)
16 18 20
0.4 0.1 0.5
(a) Compute E(X), E(X²), and V(X).
A³
E(X)=
E(X²)=
V(x)=
(b) If the price of a freezer having capacity X is 69X-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.)
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. X p(x) 16 18 20 0.4 0.1 0.5 (a) Compute E(X), E(X²), and V(X). A³ E(X)= E(X²)= V(x)= (b) If the price of a freezer having capacity X is 69X-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.)
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