توزیع یکنواخت گسسته

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

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

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

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

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

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

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

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