Abstract: The higher-order moment of sum of independent and identically distributed exponential random variables was investigated. The higher-moment of exponential random variable was computed by mathematical induction method. Base on this result, combining the multinomial theorem and the knowledge about the partition of integer in combinatorics, the higher-order moment of sum of independent and identically distributed exponential random variables was computed and the computation formula was got. At last, the conclusion was illustrated by numerical example.

Key words: Exponential distribution, Sum of random variables, Higher-order moment, Multinomial theorem, Mathematical expectation

摘要： 研究了独立同指数分布随机变量和的高阶矩。利用数学归纳法对指数分布随机变量的高阶矩进行了计算，并以此为基础，结合组合数学中的多项式定理和整数分拆的相关知识对独立同指数分布随机变量和的高阶矩进行计算，得到了其高阶矩的计算公式，并利用数值例子进行了说明。

关键词: 指数分布, 随机变量和, 高阶矩, 多项式定理, 数学期望