(統計)Discrete uniform distribution，離散型均勻分布

 

Discrete uniform distribution，離散型均勻分布

$p(x)=\left\{\begin{array}{l}\cfrac{1}{n}\ \ &，x=0,1,2,\cdots,n \\0\ \ &，o.w \end{array}\right.$

$E(x)=\displaystyle\sum_{x=1}^nx\cfrac{1}{n}=\cfrac{n(n+1)}{2}\cfrac{1}{n}=\cfrac{n+1}{2}$

$E(x^2)=\displaystyle\sum_{x=1}^nx^2\cfrac{1}{n}=\cfrac{n(n+1)(2n+1)}{6}\cfrac{1}{n}=\cfrac{(n+1)(2n+1)}{6}$

$Var(x)=\cfrac{(n+1)(2n+1)}{6}-(\cfrac{n+1}{2})^2=\cfrac{n^2-1}{12}$