Uniform Distribution

Definition

$X\sim U(a,b)$ where $a$ and $b$ are the minimum and maximum values.

Properties

PDF

$f(x)=\{\begin{array}{ll}\frac{1}{b-a}& x\in [a,b]\\ 0& \text{otherwise}\end{array}$

CDF

$F(x)=\{\begin{array}{ll}0& x<a\\ \frac{x-a}{b-a}& x\in [a,b]\\ 1& x>b\end{array}$

Mean

$E(X)=\frac{a+b}{2}$

Variance

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