Covariance of uniform distribution and it's square I have $X$ ~ $U(-1,1)$ and $Y = X^2$ random variables, I need to calculate their covariance.
My calculations are:
$$
Cov(X,Y) = Cov(X,X^2) = E((X-E(X))(X^2-E(X^2))) = E(X X^2) = E(X^3) = 0
$$
because
$$
E(X) = E(X^2) = 0
$$
I'm not sure about the $X^3$ part, are my calculations correct?

We know it is $E(X^3)$ so:
$$E(X^3)=\int_{-1}^{1}x^3f(x)=0$$
So it is correct
