The F-variate, named after the statistician Ronald Fisher, crops up in statistics in the analysis of variance (amongst other things). Suppose you have a bivariate normal di
…stribution. You calculate the sums of squares of the dependent variable that can be explained by regression and a residual sum of squares. Under the null hypothesis that there is no linear regression between the two variables (of the bivariate distribution), the ratio of the regression sum of squares divided by the residual sum of squares is distributed as an F-variate. There is a lot more to it, but not something that is easy to explain in this manner - particularly when I do not know your knowledge level. (MORE) 
