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In a piston assembly, the specifications for the clearance

Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi ISBN: 9780073401331 38

Solution for problem 4E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

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Statistics for Engineers and Scientists | 4th Edition | ISBN: 9780073401331 | Authors: William Navidi

Statistics for Engineers and Scientists | 4th Edition

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Problem 4E

In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below:

Step-by-Step Solution:

Step 1 of 2

 

Given, the number with too little clearance is X and

The number with too much clearance is Y.

Then the joint probability mass function of X and Y is given in the table below.

                      y

x

0

1

2

3

0

0.15

0.12

0.11

0.1

1

0.09

0.07

0.05

0.04

2

0.06

0.05

0.04

0.02

3

0.04

0.03

0.02

0.01

Our goal is:

     a). Find the probability mass function of X.        

     b). Find the probability mass function of Y.

     c). Are X and Y are not independent? Explain.

     d). Find mean and .

     e). Find .

     f). Find Cov (X,Y).

     g). Find .

Step 2 of 2

Chapter 2.6, Problem 4E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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In a piston assembly, the specifications for the clearance