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

## Problem 27E Chapter 2.6

Statistics for Engineers and Scientists | 4th Edition

• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants

Statistics for Engineers and Scientists | 4th Edition

4 5 0 368 Reviews
16
0
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

#### Related chapters

×
Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 2.6 - Problem 27e

Get Full Access to Statistics For Engineers And Scientists - 4th Edition - Chapter 2.6 - Problem 27e

I don't want to reset my password

Need help? Contact support

Need an Account? Is not associated with an account
We're here to help