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On the Construction of Independence Counterexamples

 

作者: BruceR. Johnson,   BenjaminJ. Tilly,  

 

期刊: The American Statistician  （Taylor Available online 1996）
卷期: Volume 50, issue 1  

页码: 14-16

 

ISSN:0003-1305

 

年代: 1996

 

DOI:10.1080/00031305.1996.10473535

 

出版商: Taylor & Francis Group

 

关键词: Counterexamples;Dependence;Independence;Random events;Teaching of mathematical statistics;Teaching of probability.

 

数据来源: Taylor

 

摘要:

A simple method of modifying probability to create independence counterexamples is given. This method can be used to construct counterexamples for finite collections of events and for infinite sequences of events. It is shown how to construct examples of countable collections of events where all equations in the (countable) family of “product rules” that define independence are satisfied except for one or, more generally, except for an arbitrarily specified subfamily.

 

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