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Let Y1 and Y2 be uncorrelated random variables and

Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer ISBN: 9780495110811 47

Solution for problem 94E Chapter 5

Mathematical Statistics with Applications | 7th Edition

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Mathematical Statistics with Applications | 7th Edition | ISBN: 9780495110811 | Authors: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer

Mathematical Statistics with Applications | 7th Edition

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Problem 94E

Problem 94E

Let Y1 and Y2 be uncorrelated random variables and consider U1 = Y1 + Y2 and U2 = Y1 − Y2.

a Find the Cov(U1, U2) in terms of the variances of Y1 and Y2.

b Find an expression for the coefficient of correlation between U1 and U2.

c Is it possible that Cov(U1, U2) = 0? When does this occur?

Step-by-Step Solution:

Solution

Step 1 of  3

a) We have to find the

Given that

                 

Now

                      =

       

                      =

                    =

                    =

We know that

                                                =

                                                 =

     

                               [  Note: since ]

                                                =

                                               = 

                                               =

Hence


Step 2 of 3

Chapter 5, Problem 94E is Solved
Step 3 of 3

Textbook: Mathematical Statistics with Applications
Edition: 7
Author: Dennis Wackerly; William Mendenhall; Richard L. Scheaffer
ISBN: 9780495110811

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Let Y1 and Y2 be uncorrelated random variables and