Uniform Distribution

Continuous uniform on $[a,b]$ with $a<b$:

$$f(x)=\frac{1}{b-a},a\le x\le b$$

Expected Value

$$\mathbb{E}[X]=\frac{a+b}{2}$$

Variance

$$\mathrm{Var}(X)=\frac{(b-a{)}^2}{12}$$