F Distribution
If $X \sim \chi_m^2$ and $Y \sim \chi_n^2$ are independent, then
$$W = \frac{X/m}{Y/n} \sim F_{m,n}.$$The F distribution is right-skewed and appears naturally when comparing scaled variance quantities. A squared $t_n$ random variable follows an $F_{1,n}$ distribution.
For $n > 2$,
$$\mathbb{E}(W) = \frac{n}{n-2}.$$