Question. Consider random variables X and Y with joint density

Evaluate Corr (X,Y).

Answer.

To use Corr (X,Y) formula, I will need to know Cov(X,Y)=E(XY)-E(X)E(Y) and Var(X) and Var(Y). This is a simple question but I keep getting negative variance for X and I re-checked several times. Help!!

(on the interval 0<x<1, and 0 otherwise)

Then

(For Y, and Var(Y)=2/75, so I should be able to proceed to find Cov and Corr if I have a positive result for Var(X)).

thanks!