Marginals of a trivariate normal

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?"

It is well known that normal marginals of a bivariate distribution
don't imply a joint normal. the previous question is to some extent a
generalization of this statement in higher dimensions.

Any insight is greatly appreciated!

-G

.

Relevant Pages

  • Re: Marginals of a trivariate normal
    ... random variables follows a bivariate normal distribution. ... sufficient to state that the joint distribution of the three random ...
    (sci.stat.math)
  • Re: Analysis Tool Pack: Random function help
    ... In Excel Help. ... Click the distribution method you want to use to create random values. ... Characterized by a probability of success on a given trial. ... Bernoulli random variables have the value 0 or 1. ...
    (microsoft.public.excel.programming)
  • Re: Renewal process
    ... be played by a geometric distribution with parameter p? ... studied "compound random variables" yet? ... enough in order to know what to take the Laplace transform? ... discarding arriving customers we put them ...
    (sci.math)
  • Re: MLE Related Proof
    ... #3) The pdfs all have the same common support. ... Lindeberg-Levy thm is invoked to get the limiting distribution of the ... that f represents the distribution of the random variables X1, ... Kullback-Leibler distance ...
    (sci.stat.edu)
  • Re: An optimization problem
    ... generates a realization of the N random variables according to their ... probability distribution. ... but it's fairly easy to get a Monte Carlo approximation for it. ...
    (sci.math)
Loading