Independent events in elementary probability theory
Independent events in elementary probability theory
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初等概率论中的独立事件
DOI：
10.1080/0020739x.2011.562313
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发表时间：
2011
影响因子：
0.9
通讯作者：
A. Csenki
中科院分区：
文献类型：
--
作者：
A. Csenki
在概率和统计教数学家作为第一次介绍或非数学观众，联合独立的事件是通过要求乘法规则得到满足。下面的陈述通常被默认为成立（并且，最好的情况下，直观地动机）：如果n个事件E1，E2，.，En是联合独立的，那么从{E1，E2，.，En}的两个不相交的子集中以多个步骤构建的任何两个事件A和B也是独立的。只有在形成事件A和B时才允许运算“并”、“交”和“补”。在这里，我们从初等概率论的观点来考察这一陈述。这里所描述的方法也是用户的概率论，被认为是新颖的。
In Probability and Statistics taught to mathematicians as a first introduction or to a non-mathematical audience, joint independence of events is introduced by requiring that the multiplication rule is satisfied. The following statement is usually tacitly assumed to hold (and, at best, intuitively motivated): If the n events E 1, E 2, … , E n are jointly independent then any two events A and B built in finitely many steps from two disjoint subsets of {E 1, E 2, … , E n } are also independent. The operations ‘union’, ‘intersection’ and ‘complementation’ are permitted only when forming the events A and B. Here we examine this statement from the point of view of elementary probability theory. The approach described here is accessible also to users of probability theory and is believed to be novel.