Variance of F-Distribution

Theorem
Let $n, m$ be strictly positive integers.

Let $X \sim F_{n, m}$ where $F_{n, m}$ is the F-distribution with $\tuple {n, m}$ degrees of freedom.

Then the variance of $X$ is given by:


 * $\var X = \dfrac {2 m^2 \paren {m + n - 2} } {n \paren {m - 4} \paren {m - 2}^2}$

for $m > 4$, and does not exist otherwise.