[Math] find cov(Y1,Y1) given expected value and variance

probabilitystatistics

I am given two random variables $Y_1$ and $Y_2$ and:

  • $E(Y_1) = 4$
  • $E(Y_2) = -1$
  • $V(Y_1) = 2$
  • $V(Y_2) = 8$

I am asked to find $Cov(Y_1,Y_1)$

I know $Cov(Y_1,Y_2) = E(Y_1Y_2)-E(Y_1)E(Y_2)$

I'm not sure if it is a typo, but it says $Cov(Y_1,Y_1)$ NOT $Cov(Y_1,Y_2)$

The answer is $2$, but i'm not sure how to get $E(Y_1Y_2)$ from the information given, or why it's asking for the Cov of the same variable?

Thanks for any help!

Best Answer

$cov(Y_1,Y_1)=var(Y_1)=2$ 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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