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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^22*p*x*y)] 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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