关键词: 指数分布, 随机变量和, 高阶矩, 多项式定理, 数学期望

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