| 关于随机事件与随机变量独立性的注记 |
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| 引用本文： | 彭英. 关于随机事件与随机变量独立性的注记[J]. 湖南师范大学自然科学学报, 1988, 0(1) |
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| 作者姓名： | 彭英 |
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| 作者单位： | 湖南师范大学数学系 |
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| 摘 要： | 本文对S.Bernstein提供的三个两两独立,但不彼此独立的离散随机变量的集合,推广到n个连续型随机变量的情形,即使它的一切真子集独立,但它仍不独立;同时,还用初等的方法构造了一个n>3个的随机事件的一切真子集是独立的,但总体不独立的例。
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| 关 键 词： | 独立性 随机变量 随机参数/随机事件 |
A NOTE ON INDEPENDENCE OF RANDOM EVENTS AND RANDOM VARIABLES |
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| Peng Ying. A NOTE ON INDEPENDENCE OF RANDOM EVENTS AND RANDOM VARIABLES[J]. Journal of Natural Science of Hunan Normal University, 1988, 0(1) |
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| Authors: | Peng Ying |
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| Affiliation: | Peng Ying Department of Mathematics |
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| Abstract: | The example of a set of discrete variates that are pairwise independent but not mutuallyindependent usually quoted in statistical literature is due to S.Bernstein.In this paper,S.Bernstein's example has been extended to n>3 and continuous variate case.Moreover,by an elementary method,we have constructed an example in which all proper subsets ofn>3 random events are independent but the events are not mutually independent. |
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| Keywords: | independence random variable random parameter/random event |
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