# F-distribution

In statistics, the**is the probability distribution of a random variable of the form**

*F*-distribution

*U*_{1}and*U*_{2}have chi-square distributions with*d*_{1}and*d*_{2}degrees of freedom respectively, and*U*_{1}and*U*_{2}are independent (see Cochran's theorem for an application).

*F*-distribution arises frequently as the null distribution of a test statistic, especially in likelihood-ratio tests, perhaps most notably in the analysis of variance.

If *d*_{2} > 2, then the mean is *d*_{2}/(*d*_{2} − 2) and
if *d*_{2} > 4 the variance is given by

*d*

_{1}> 2, it is a unimodal with mode