F distribution

(Also called the Fisher-Snedecor Distribution): if X₁ and X₂ are random variables that follow normal distributions with arbitrary means and variances and , and if samples of sizes N₁ and N₂ are drawn from the two distributions, then

are unbiased estimators of the variances. The quantities

chi-square distributions with f₁=N₁-1 and f₂=N₂-1 degrees of freedom, respectively.

The quotient

is described by the F distribution with (f₁,f₂) degrees of freedom. It has the probability density function

and the properties 3pt

In the limit the product f₁F approaches the chi-square distribution with f₁ degrees of freedom.