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. 16 18 20 p(x) 0.3 0.1 0.6 (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 67X – 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? ft3
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. 16 18 20 p(x) 0.3 0.1 0.6 (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 67X – 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? ft3
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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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.
16
18
20
p(x)
0.3
0.1
0.6
(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 67X – 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?
ft3
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