二项分布高阶原点矩的一种简便算法

Simple Algorithm for the Binomial Distribution Moments on the Origin of Higher-Order

考虑到直接用定义计算二项分布高阶原点矩的复杂性,将组合数学中的第二类Stirling数应用到概率中,给出了利用第二类Stirling数求二项分布m阶原点矩的方法:,并用实例对此方法进行了验证。

Considering the complexity on calculating the binomial distribution moments on the origin of higher--order with definition, Stifling number of the second kind of combinatorics was applied to probability. And a method in which Stiflingnumber of the second kind was used was given to solve this problem： EX^m=∑^m/l=0S（m,l）[n]lP^l. Moreover, the method wastested by an example.