My Math Forum is this gaussian?

 January 25th, 2010, 12:22 PM #1 Newbie   Joined: Jan 2010 Posts: 1 Thanks: 0 is this gaussian? Is the following density gaussian?: Code: f(x,y)=A*exp[-1/2*(x^2+y^2-2*p*x*y)] where A is the appropriate normalizing constant and p is the correlation between x and y. The marginal densities for x and y are indeed normal. I have a book that claims it 2d gaussian, but I can't figure out what the covariance matrix would be... it isn't [[1 p] [p 1]] because f doesn't have the 1/(1-p^2) in the denominator of the exponential... help? More general question: are all exponentials of quadratic functions gaussian? This seems to be true for the univariate case but can't confirm for multivariate.
 January 25th, 2010, 01:19 PM #2 Global Moderator   Joined: May 2007 Posts: 6,762 Thanks: 697 Re: is this gaussian? Let y=px+u. Then As a function of x and u you will have two independent Guassian terms. I'll confess to being a little rusty here, so I'll let you work out the details. As for your second question, the answer is yes except for singularities (such as p=1).

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