条件概率的弱定义与随机事件间相依性的不同刻画

A Weak Definition of Conditional Probability and Different Depicts to the Dependence of Random Events

从不同角度刻画任意两个随机事件之间的相依关系是更一般的准确刻画随机变量之间的相依关系的前提.基于积事件概率不等式,提出了条件概率的弱定义、事件间的相依原理和事件间的相依度,并利用定性与定量方法相结合逐步深入刻画了任意两个随机事件之间的相依关系.同时,推广了条件概率、独立性等概念与相关概率命题的适用范围,使相关结论在具有理论价值和实践价值基础上,有更完美、对称的表达形式.

In order to accurately describe the dependent relationship between random variables in general,it is the premise to describe the dependent relationship between random events from different angles.Based on the product event probability inequality,a weak definition of conditional probability is proposed,which is convenient to describe the dependent relationship and the dependent measure between any two random events through qualitative and quantitative analysis.The application scope of conditional probability and independence and related probability proposition has been expanded,so that the relevant conclusions would have a more perfect and symmetrical expression on the basis of theoretical value and practical value.