توزیع یکنواخت گسسته

${\displaystyle P(X)={\begin{cases}1/(a-b)&{\text{if }X{\text{ is in [a,b]}\\0&{\text{Otherwise}\end{cases}$

${\displaystyle C(X)={\begin{cases}0&X<a\\{\frac {\left\lfloor X\right\rfloor -a+1}{b-a+1},&X{\text{ in }[a,b]\\1&X>b\end{cases}$

${\displaystyle E(X)=\sum _{x=a}^{b}\displaystyle xP(x)=1/(b-a+1)\sum _{x=a}^{b}x}$

${\displaystyle =1/(b-a+1){\biggl (}(b+a)(b-a+1)/2{\Bigr )}$

${\displaystyle =(b+a)/2}$

${\displaystyle V(X)=\sum _{x=a}^{b}P(x)(x-E(X))^{2}$

${\displaystyle =1/(b-a+1)){\biggl (}\sum _{x=a}^{b}(x-{\frac {b+a}{2})^{2}{\Bigr )}$

${\displaystyle ={\frac {(b-a)^{2}{12}$