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I am given two random variables Y1 and Y2 and: E(Y1) = 4 E(Y2) = -1 V(Y1) = 2 V(Y2) = 8

I am asked to find Cov(Y1,Y1)

I know Cov(Y1,Y2) = E(Y1Y2)-E(Y1)E(Y2)

I'm not sure if it is a typo, but it says Cov(Y1,Y1) NOT Cov(Y1,Y2)

The answer is 2, but i'm not sure how to get E(Y1Y2) from the information given, or why it's asking for the Cov of the same variable?

Thanks for any help!

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2 Answers 2

up vote 2 down vote accepted

$cov(Y_1,Y_1)=var(Y_1)=2$ This follows from the definition of covariance:

$cov(Y_1,Y_1)=E(Y_1\cdot Y_1)-E(Y_1)E(Y_1)=E(Y_1^2)-E(Y_1)^2$

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love how it says that nowhere in my book... Thanks! –  kralco626 Nov 17 '10 at 2:38
    
This follows from the definition. See above edit. –  Timothy Wagner Nov 17 '10 at 2:42

Cov$(Y_1,Y_2) = \text{Cov}((Y_1-E[Y_1])(Y_2-E[Y_2])) = E[Y_1 Y_2]-E[Y_1]E[Y_2]$

Now let $Y_2 = Y_1$

Then Cov$(Y_1,Y_2) = E[{Y_1}^2] -(E[Y_1])^2$

This equation should look familiar...the variance of $Y_1$

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nicely explained –  kralco626 Nov 17 '10 at 3:30

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