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An certain brand of upright freezer is available in three different rated capacities: 16 ft, 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) 0.4 0.3 0.3 (a) Compute E(X), E(X?), and V(X). | ft³ E(X) = E(x?) = V(X) = (b) If the price of a freezer having capacity X is 62X – 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?

An certain brand of upright freezer is available in three different rated capacities: 16 ft, 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) 0.4 0.3 0.3 (a) Compute E(X), E(X?), and V(X). | ft³ E(X) = E(x?) = V(X) = (b) If the price of a freezer having capacity X is 62X – 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?

A First Course in Probability (10th Edition)
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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An certain brand of upright freezer is available in three different rated capacities: 16 ft, 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) 0.4 0.3 0.3 (a) Compute E(X), E(X?), and V(X). | ft³ E(X) = E(x?) = V(X) = (b) If the price of a freezer having capacity X is 62X – 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) = Xx – 0.009x2. What is the expected actual capacity of the freezer purchased by the next customer? ] ft³
Transcribed Image Text:An certain brand of upright freezer is available in three different rated capacities: 16 ft, 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) 0.4 0.3 0.3 (a) Compute E(X), E(X?), and V(X). | ft³ E(X) = E(x?) = V(X) = (b) If the price of a freezer having capacity X is 62X – 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) = Xx – 0.009x2. What is the expected actual capacity of the freezer purchased by the next customer? ] ft³
Expert Solution
Step 1

We know that 

E(x)=∑xp(x)

E(x2)=∑x2p(x)

Var(x) = E(x2) - [E(x)]2

 

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