3
$\begingroup$

If X and Y are standardized variables and are perfectly positively correlated with respect to each other, how can i prove that $E[(X-Y)^2] = 0$?

$\endgroup$

1 Answer 1

12
$\begingroup$

$E[(X-Y)^2) = E(X^2) + E(Y^2) - 2E(XY)$

Use the fact that $X, Y$ are standardized and perfectly correlated to make appropriate substitutions above to get the desired result.

PS: I am not providing the complete solution. Hopefully, the above hints will set you on the right path.

$\endgroup$
3
  • $\begingroup$ I know that E(XY) is 1 (this is the correlation), so E(X^2)+E(Y^2) must equal 2 but I'm having trouble showing this. $\endgroup$ Nov 1, 2010 at 23:29
  • 3
    $\begingroup$ Can you connect E(X^2) to the variance formula? $\endgroup$
    – user28
    Nov 1, 2010 at 23:31
  • $\begingroup$ Ahh so E(X^2) = Variance(X) when the mean is 0, and so variance is 1. $\endgroup$ Nov 1, 2010 at 23:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.