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