关于随机变量期望方差的两个注记  

Two Notes on the Expectation and Variance of Random Variables

作　　者：徐亚茹 徐晓岭 顾蓓青 XU Yaru;XU Xiaoling;GU Beiqing(School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China)

机构地区：[1]上海对外经贸大学统计与信息学院,上海201620

出　　处：《高等数学研究》2022年第1期10-12,共3页Studies in College Mathematics

摘　　要：文献[1]中给出了有关条件期望与三个随机变量独立的两个充要条件,本文通过几个反例说明其充分性是不成立的.分析了文献[4]中一个定理证明存在的错误,并给出了新的证明.Two necessary and sufficient conditions for conditional expectation and independence of three random variables are given in the reference[1].Several counter examples are given to illustrate that their sufficiency is not valid in this paper.Besides,an error in the proof of a theorem in reference[4]is analyzed,and a new proof is proposed.

关 键 词：期望 独立性 充要条件 充分条件 

分 类 号：O211.1[理学—概率论与数理统计]