分布可加性的教学注记  

Teaching Notes on Additive Property of Distribution

作　　者：王勇智[1] 杨国庆 花虹[1] WANG Yongzhi;YANG Guoqing;HUA Hong(School of Mathematical Sciences,Tongji University,Shanghai 200092,China)

机构地区：[1]同济大学数学科学学院,上海200092

出　　处：《高等数学研究》2023年第1期51-56,75,共7页Studies in College Mathematics

基　　金：同济大学第十七期实验教学改革专项基金项目(No.36)。

摘　　要：本文先给出二项分布以及正态分布可加性的几种证明方法,包括构造法、特征函数法和母函数法等.在此基础上得到了随机变量的特征函数和整值随机变量的母函数满足一定形式时分布具有可加性的充分条件.最后给出了常用随机变量特征函数和母函数,并分析了使用构造法证明可加性的充分条件.In this paper, we first present several methods to prove the additive property of binomial distribution and normal distribution, including construction method, characteristic function method, and generating function method.Based on these, some sufficient conditions of additive property of distributions are obtained when the characteristic functions of random variables and the generating functions of integer valued random variables satisfy certain forms.Finally, the characteristic functions and generating functions of some commonly used random variables are given, and the sufficient conditions of additive property proved by construction method are analyzed.

关 键 词：可加性 特征函数 母函数 

分 类 号：O211[理学—概率论与数理统计]