# 離散型均勻分佈

參數 n=5 where n=b-a+1概率質量函數 累積分佈函數 ${\displaystyle a\in (...,-2,-1,0,1,2,...)\,}$${\displaystyle b\in (...,-2,-1,0,1,2,...)\,}$${\displaystyle n=b-a+1\,}$ ${\displaystyle k\in \{a,a+1,...,b-1,b\}\,}$ ${\displaystyle {\begin{matrix}{\frac {1}{n}}&{\mbox{for }}a\leq k\leq b\ \\0&{\mbox{otherwise }}\end{matrix}}}$ ${\displaystyle {\begin{matrix}0&{\mbox{for }}kb\end{matrix}}}$ ${\displaystyle {\frac {a+b}{2}}\,}$ ${\displaystyle {\frac {a+b}{2}}\,}$ N/A ${\displaystyle {\frac {n^{2}-1}{12}}\,}$ ${\displaystyle 0\,}$ ${\displaystyle -{\frac {6(n^{2}+1)}{5(n^{2}-1)}}\,}$ ${\displaystyle \ln(n)\,}$ ${\displaystyle {\frac {e^{at}-e^{(b+1)t}}{n(1-e^{t})}}\,}$ ${\displaystyle {\frac {e^{iat}-e^{i(b+1)t}}{n(1-e^{it})}},}$

${\displaystyle F(k;a,b)={\frac {\lfloor k\rfloor -a+1}{b-a+1}}}$