独立同均匀分布随机变量和的高阶矩的计算

摘要

Considering the importance of uniform distribution and the higher-order moment of sum of random variables, the higher-order moment of sum of i. i. d U( 0,1) random variables is computed by multinomial theorem and Stirling number of the second kind in combinatorics. The computational formula is got Base on this formula and binomial theorem, the formula of the higher-moment of sum of i. i. d I/(a,b) random variables is got. At last, some examples are given.%考虑到均匀分布与随机变量和的高阶矩的重要性,利用组合数学中的多项式定理和第二类Stirling数对独立同U(0,1)随机变量和的高阶矩进行了计算,得到了相应的计算公式.并以此为基础利用二项式定理,得到了独立同U(a,b)随机变量和的高阶矩的计算公式.最后给出了计算实例.