The Chi-Squared Distribution

parameter ν

4

mean:	ν	=	4
variance:	2ν	=	8
moment generating function:	-ν/2 (1-2t)	=	1 2 (1-2t)

The sum of

ν

squares of independent standard normal random variables is a chi-squared random variable with

ν

degrees of freedom. This distribution is a special case of the gamma distribution that arises in statistics when estimating the variance of a population. The red vertical line marks the mean of the distribution.