Chi

The Chi random variable with $ N$ degrees of freedom is

$\displaystyle t = \sum_{i=1}^N \; \vert x_i\vert,
$

The mean of $ t$ is

$\displaystyle \mu = {\cal E}\{t\}=\sqrt{2/\pi} N\sigma,$

and the variance of $ t$ is

$\displaystyle {\cal E}\{(t-\mu)^2\}=N\sigma^2-\mu^2.$

If $ N=1$,

$\displaystyle \log p(t)= \frac{1}{2} \log\left({2\over \pi} \right) - \frac{t^2}{2}.$



Baggenstoss 2017-05-19