| 关于随机变量期望方差的两个注记 |
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| 引用本文： | 徐亚茹,徐晓岭,顾蓓青. 关于随机变量期望方差的两个注记[J]. 高等数学研究, 2022, 25(1): 10-12. DOI: 10.3969/j.issn.1008-1399.2022.01.004 |
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| 作者姓名： | 徐亚茹 徐晓岭 顾蓓青 |
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| 作者单位： | 上海对外经贸大学统计与信息学院,上海201620 |
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| 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.
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| 关 键 词： | 期望 独立性 充要条件 充分条件 |
Two Notes on the Expectation and Variance of Random Variables |
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| XU Yaru,XU Xiaoling,GU Beiqing. Two Notes on the Expectation and Variance of Random Variables[J]. Studies In College Mathematics, 2022, 25(1): 10-12. DOI: 10.3969/j.issn.1008-1399.2022.01.004 |
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| Authors: | XU Yaru XU Xiaoling GU Beiqing |
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| Affiliation: | (School of Statistics and Information, Shanghai University of International Business and Economics, Shanghai 201620, China) |
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| Abstract: | 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. |
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| Keywords: | expectation independence necessary and sufficient condition |
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