<p><a href="https://stats.stackexchange.com/questions/81469/if-any-two-variables-follow-a-normal-bivariate-distribution-does-it-also-have-a">This question</a> was marked as a duplicate of <a href="https://stats.stackexchange.com/questions/30159/is-it-possible-to-have-a-pair-of-gaussian-random-variables-for-which-the-joint-d">this</a> question.</p>

<p>However, they are <em>not</em> asking the same question, and I think that unless the answers at the supposed duplicate are altered to respond to this question, they don't actually answer it.</p>

<p>The question is asking about a trivariate where all of the bivariate margins are bivariate normal. The question it's marked as a duplicate of is asking about a <em>bivariate</em> where the <em>univariate</em> margins are normal.</p>

<p>An answer to the question "<em>Is it possible to have a pair of Gaussian random variables for which the joint distribution is not Gaussian?</em>" does not of itself necessarily imply the same answer to the question about bivariate margins of a trivariate distribution. It's a rather subtler question, and the counterexample somewhat more complex than the counterexamples for the supposed duplicate.</p>

<p>While the answers could be extended to answer this question, as far as I can see they currently don't.</p>

<p>When it first came up for closure (a couple of weeks ago), I responded (via a comment) pointing out the difference. I've only just noticed that it was voted for closure in spite of the comment.</p>

<p>I've just nominated to reopen, but apparently my original comment was insufficient, so I raise it here, in the hope that we can resolve this question.</p>
