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Let X and Y be random variables, and a and b be

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

Solution for problem 27E 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 27E

Let X and Y be random variables, and a and b be constants.

a. Prove that Cov(aX, bY) = ab Cov(X, Y).

b. Prove that if a > 0 and b > 0, then ρaX,bY = ρX,Y. Conclude that the correlation coefficient is unaffected by changes in units.

Step-by-Step Solution:

Step 1 of 2:

Let X and Y be the random variable.

Our goal is :

a). We need to prove that Cov(aX,bY)=abCov(X,Y).

b). We need to prove that if a>0 and b>0,then  .

a).

Now we need to prove that Cov(aX,bY)=abCov(X,Y)

Here a and b are the constants.

Here

and

Then,

Here

Therefore

Step 2 of 2

Chapter 2.6, Problem 27E is Solved
Textbook: Statistics for Engineers and Scientists
Edition: 4
Author: William Navidi
ISBN: 9780073401331

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