# Variance of uniform distribution

From timescalewiki

** Proposition:** Let $X$ have the uniform distribution on $[a,b] \cap \mathbb{T}$. Then,
$$\mathrm{Var}_{\mathbb{T}}(X)=2\dfrac{h_3(\sigma(b),0)-h_3(a,0)}{\sigma(b)-a}-\left( \dfrac{h_2(\sigma(b),a)}{\sigma(b)-a}+a \right)^2.$$

**Proof:** █