1
$\begingroup$

If
$X \sim N(0,{a^2})$,
$Y \sim N(0,{b^2})$ and
$Corr(X,Y) = \rho $,
then can we say that $(X,Y) \sim BVN(0,0,{a^2},{b^2};\rho )$?

If this is true, then can someone please tell me how can I proceed to show this mathematically?

Thanks!

$\endgroup$