\begin{definition}[Definition:F-Distribution]
Let $X$ be a continuous random variable on a probability space $\struct {\Omega, \Sigma, \Pr}$.
Let $\Img X = \hointr 0 \infty$. 
Let $n, m$ be strictly positive integers.
$X$ is said to have an '''F-distribution''' with $\tuple {n, m}$ degrees of freedom {{iff}} it has probability density function:
:$\map {f_X} x = \dfrac {m^{m / 2} n^{n / 2} x^{\paren {n / 2} - 1} } {\paren {m + n x}^{\paren {n + m} / 2} \map \Beta {n / 2, m / 2} }$
where $\Beta$ denotes the beta function. 
This is written: 
:$X \sim F_{n, m}$
\end{definition}