Covariance of Two Dependent Variables So I'm looking at the following:
$\operatorname{Cov}(X, X^2)$ where $X$ is the standard normal.  So I know that $E[X] = 0$ and we have:
$$\operatorname{Cov}(X, X^2) = E(X \cdot X^2) - E[X] \cdot E[X^2] = E[X^3] - 0 \cdot E[X^2] = E[X^3]$$
From googling around, apparently this $= 0$, but I'm not sure why.
Any clarification here?
Thanks,
Mariogs

The standard normal distribution (probability distribution function $\frac{e^{-\frac{1}{2}x^2}}{\sqrt{2\pi}}$) is symmetric around $x=0$, since $x^3$ is antisymmetric, $E[X^3]=0$.
