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 April 17th, 2009, 12:33 PM #1 Newbie   Joined: Apr 2009 Posts: 1 Thanks: 0 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: $X = \left[ \begin{array}{c} x_1 \\ x_2 \\ \vdots \\ x_n \end{array} \right] \ \ \ \ \ \ \ \ \ \ x_1 \tilde \ N(\mu_1, \sigma_1^2), \ x_2 \tilde \ N(\mu_2, \sigma_2^2), \ \cdots, \ x_n \tilde \ N(\mu_n, \sigma_n^2) \\ Y = \sqrt{X^TX} = \sqrt{x_1^2 + x_2^2 + \cdots + x_n^2}$ 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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