Re: Marginals of a trivariate normal


"paleostat" <paleologo@xxxxxxxxx> wrote in message
news:1190320449.506630.71950@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxx
I am trying to get clarity on the following problem, which was posed
to me by a friend (who claims to be the orignal formulator!). It's
very simple to state, but I am stuck. The answer is not known to me.
Here it is:


"Consider three random variables, X, Y, Z. we assume that each pair of
random variables follows a bivariate normal distribution. Is this
sufficient to state that the joint distribution of the three random
variables is normal?"


No. Hint for counter-example: Let f(x,y,z) = exp(-x*x-y*y-z*z) if xyz > 0,
else f(x,y,z) = 0.

Graham Jones



.

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