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Transformation of a gaussian [closed]

If v~N(0,S), [S is diagonal] [normal multivariate distribution with zero mean and diagonal co-variance matrix]

What is the probability density function of v'v (the inner product between v transpose and v)?

Thanks!

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en.wikipedia.org/wiki/Chi-squared_distribution – suVRit Dec 28 2011 at 17:28
Thanks! I somehow didn't recall the fact that jointly normal uncorrelated variables are independent... – Jabob Dec 28 2011 at 20:30
actually, it isn't exactly Chi-squared distribution, as the variances are different (these are not standard normal variables), but it's a private case of generalized Chi-squared. Jabob – Jabob Jan 1 2012 at 13:31