Expectation 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 expectation of $X$ is given by:


 * $\expect X = \dfrac m {m - 2}$

for $m > 2$, and does not exist otherwise.