|Probability density function |Cumulative distribution function
|Parameters||(degrees of freedom)| |MGF||Complicated (see text)|
|CF||Complicated (see text)| |This article does not cite any
references or sources. (October 2009)| In probability theory and
statistics, the chi distribution is a continuous probability
distribution. It is the distribution of the square root of the
sum of squares of independent random variables having a standard
normal distribution. The most familiar example is the Maxwell
distribution of (normalized) molecular speeds which is a chi
distribution with 3 degrees of freedom (one for each spatial
coordinate). If are k independent, normally distributed random
variables with means and standard deviations , then the
statistic is distributed according to the chi distribution.
Accordingly, dividing by the mean of the chi distribution
(scaled by the square root of n − 1) yields the correction
factor in the unbiased estimation of the standard deviation of
the normal distribution. The chi dist