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?
Conditions for two normal R.Vs to satisfy bivariate normal distribution
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probability
probability-distributions
normal-distribution
1 Answers
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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.)