I'm a little puzzled by the whole random variable thing.
I've got two random variables, $\mathcal{X}$ and $\mathcal{N}$, both with gaussian distribution with mean = 0 and $\sigma_{\mathcal{X}}^2$ and $\sigma_{\mathcal{N}}^2$ respectively.
The equation for correlation coefficient is
$$ \rho_{XY} = E\left[\frac{X-E[X]}{\sigma_{\mathcal{X}}}\frac{Y-E[Y]}{\sigma_{\mathcal{N}}}\right] $$
I know how to find $E$ but what value do $\mathcal{X}$ and $\mathcal{N}$ actually have that I plug into the equation?