A random variate X
- will have F-distribution (with parameters d1 and d2)
where
- U1 and U2 have chi-squared distributions with d1 and d2 degrees of freedom respectively, and
- U1 and U2 are independent.
With a density of:
where 
is the gamma function.
Proof:
Larsen, R. J., & Marx, M. L. (2010). Introduction to Mathematical Statistics and Its Applications (5 edition.). Boston: Pearson.
and
http://webpages.math.luc.edu/~jdg/w3teaching/stat_305/sp06/pdf/densityF.pdf
