If I know that $A \sim \mathcal N(0,\sigma^2_A)$ and $B \sim \mathcal N(0,\sigma^2_B)$ and that $A$ and $B$ have a correlation coefficient of $\rho$, does this mean that it must be that case that
$\begin{bmatrix} A \\ B \end{bmatrix} \sim \mathcal N\left( \begin{bmatrix} 0 \\ 0 \end{bmatrix}, \begin{bmatrix} \sigma^2_A & \rho \sigma_A \sigma_B \\ \rho \sigma_A \sigma_B & \sigma_B^2 \end{bmatrix} \right) \>?$
Or is that just one possibility?
And what about for other distributions?