Homework4Solutions

Homework4Solutions - Steven Weber Dept. of ECE Drexel...

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Steven Weber Dept. of ECE Drexel University ENGR 361: Statistical Analysis of Engineering Systems (Spring, 2008) Homework 4 Solutions (Monday, April 21) Question 1: Exercise 32, § 3.3, p.107 An appliance dealer sells three diﬀerent models of upright freezers having 13.5, 15.9 and 19.1 cubic feet of storage space, respectively. Let X = the amount of storage space purchased by the next consumer to buy a freezer. Suppose that X has pmf x 13 . 5 15 . 9 19 . 1 p ( x ) 0 . 2 0 . 5 0 . 3 (1) a. Compute E [ X ] , E [ X 2 ] , and Var( X ) . E [ X ] = 0 . 2 · 13 . 5 + 0 . 5 · 15 . 9 + 0 . 3 · 19 . 1 = 16 . 38 E [ X 2 ] = 0 . 2 · 13 . 5 2 + 0 . 5 · 15 . 9 2 + 0 . 3 · 19 . 1 2 = 272 . 298 Var( X ) = E [ X 2 ] - E [ X ] 2 = 272 . 298 - 16 . 38 2 = 3 . 9936 (2) b. If the price of a freezer having capacity X cubic feet is 25 X - 8 . 5 , what is the expected price paid by the next customer to buy a freezer? E [25 X - 8 . 5] = 25 E [ X ] - 8 . 5 = 25 · 16 . 38 - 8 . 5 = 401 . (3) c. Suppose that although the rated capacity of a freezer is

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This note was uploaded on 06/24/2008 for the course ENGR 361 taught by Professor Eisenstein during the Spring '04 term at Drexel.

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Homework4Solutions - Steven Weber Dept. of ECE Drexel...

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