Variance of Student's t-Distribution

Theorem
Let $k$ be a strictly positive integer.

Let $X \sim t_k$ where $t_k$ is the $t$-distribution with $k$ degrees of freedom.

Then the variance of $X$ is given by:


 * $\var X = \dfrac k {k - 2}$

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