Bayesian Statistics: An Introduction, 4th Edition

A.2 Chi-squared distribution

X has a chi-squared distribution on ν degrees of freedom, denoted

if it has the same distribution as

where are independent standard normal variates, or equivalently if it has density

If Y=X/S, where S is a constant, then Y is a chi-squared variate on ν degrees of freedom divided by S, denoted

and it has density

The mean and variance are

The mode is

and the approximate relationship between mean, mode and median implies that the median is approximately

at least for reasonably large ν, say .