两个独立同分布的随机变量其和与差的独立性的探讨  

On Independence of the Sum and the Difference of Two Independent and Identically Distributed Random Variables

作　　者：张娟娟 周淑娟 ZHAGN Juanjuan;ZHOU Shujuan(Mathematics and Statistical Institute,Qingdao University,Qingdao 266071,China)

机构地区：[1]青岛大学数学与统计学院,山东青岛266071

出　　处：《高等数学研究》2022年第4期81-83,共3页Studies in College Mathematics

基　　金：青岛大学在线开放课程建设项目(41317030002).

摘　　要：本文围绕两个独立同分布的随机变量其和与差的独立性问题展开探讨.对于五种常见的分布,结合实例说明了两个相互独立的随机变量其和与差不独立;对于两个独立同分布的正态随机变量,证明了其和与差是相互独立的.In this paper,the independence of the sum and the difference of two independent and identically distributed random variables is discussed.For the five well-known distributions,we give specific examples to show that the sum and the difference of two independent and identically distributed random variables are not independent.For two independent and identically distributed normal random variables,we prove that the sum and the difference are independent.

关 键 词：随机变量 独立性 

分 类 号：O171[理学—数学]