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January 25th, 2010, 12:22 PM   #1
Joined: Jan 2010

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is this gaussian?

Is the following density gaussian?:
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.
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January 25th, 2010, 01:19 PM   #2
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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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