Transformation of a gaussian

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!

flag	asked Dec 28 2011 at 16:56 Jabob 1

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

closed as too localized by suVRit, Deane Yang, Ryan Budney, Ian Agol, Andres Caicedo Dec 29 2011 at 6:55

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