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Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 5 - Problem 94e
Get Full Access to Mathematical Statistics With Applications - 7 Edition - Chapter 5 - Problem 94e

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# Let Y1 and Y2 be uncorrelated random variables and

ISBN: 9780495110811 47

## Solution for problem 94E Chapter 5

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

Step 3 of 3

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