# Conditions for two normal R.Vs to satisfy bivariate normal distribution

I have to Normally distributed Random Variables X and Y which are correlated. What conditions should they satisfy so that their joint distribution is a bivariate Normal distribution?

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A necessary and sufficient condition is that, for every $(a,b)$, the linear combination $aX+bY$ is normal. (Recall that, by convention, every Dirac distribution is normal, with variance zero.)