条件期望与三变量独立性的两个充要条件

Conditional Expectation and Necessary and Sufficient Conditions about Independence of Random Variables

随机事件的独立性、随机变量的独立性是概率统计中的重要概念,不少学者都在这方面有所讨论.本文作者讨论了三维连续型随机变量(X,Y,Z)中三个分量X,Y,Z的相互独立性、条件独立性,得到三个引理.利用条件期望及三个引理作者给出了三变量相互独立的两个充要条件.

The independence of the random event and the random variable are important concepts.Many scholars have discussion in these aspects.In this article,the author discusses the mutual dependence and conditional independence of three components in the three dimensional continuous r.v（X,Y,Z）.The author demonstrates three lemmas.By using the conditional expectation and three lemmas,the author gives two necessary and sufficient conditions about mutual independence of three random variables.