华东师范大学学报(自然科学版) ›› 2003, Vol. 2003 ›› Issue (4): 19-24.

• 论文 • 上一篇    下一篇

一类连续事件独立性问题的研究

万福永1,徐和坤2   

  1. 1.华东师范大学 数学系,上海 200062;2.华东师范大学 数理统计系,上海 200062
  • 收稿日期:2002-01-20 修回日期:2002-04-17 出版日期:2003-12-25 发布日期:2003-12-25

Study on the Independentce of Continuouse Events

WAN Fu-yong1;XUH-kun2   

  1. 1.Departmengt of Mathematics,East China Normal University,Shanghai 20062,China 2.Departmengt of Statistics East China Normal University,Shanghai 20062,China
  • Received:2002-01-20 Revised:2002-04-17 Online:2003-12-25 Published:2003-12-25

摘要： 作者从数学实验的一个系列实例出发,逐步深入地探索了两事件A、B的独立性与概率P(AB)、P(A)·P(B)的关系,特别是关于连续事件A、B的P(AB)与P(A)·P(B)的关系给出了一个从相关、到独立、再相关的典型实例.研究表明,事件的相关性也有一个从量变到质变的过程.

关键词: MonteCarlo方法, 连续事件, 独立性, 量变到质变, MonteCarlo方法, 连续事件, 独立性, 量变到质变

Abstract: In this paper, the relation between the independence of events and the probabilities of them is discussed from a series of mathematical experiments.We mainly focus on the case of continuous events. A typical example was given from correlation to independence.Our results show that there is a process from quantitative changes to qualitative changes for the correlation of events.

Key words: continuous events, ndependence, from quantitative change to qualitative change, MonteCarlo methods, continuous events, ndependence, from quantitative change to qualitative change