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April 17th, 2009, 11:33 AM   #1
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PDF of the 2-norm

Hi,

I need to find the probability density function of the 2-norm of a vector. I actually just need the mean and covariance, but unless there is a more straight-forward way, I was just going to calculate the moments. Here is the problem:



What is the probability density function of Y? If the n-vector is untenable, then I really need it for the 3-vector. Assume the the elements of X are independent.

I did this for the scalar case (absolute value) and got the pdf as well as the mean and covariance in closed form. However, I have not been able to get even the 2-vector case.
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