条件数学期望与随机变量独立性的一个充要条件

Independence of Random Variables and a Necessary and Sufficient Condition

随机试验的独立性、随机事件的独立性、随机变量的独立性均是概率统计中的重要概念,不少学者都在这些方面有所讨论.本文作者就二维离散形随机向量(ξ,η)中两个分量ξ与η的相互独立性展开讨论.先是证明了三个引理,其中引理1在一般概率论教科书中均有介绍,但为使读者方便,作者也作了证明.利用三个引理,作者找到随机变量独立性的一个充要条件.

In probability and statistics, the independence of random trial, the independence of random event and the independence of random variable are all important concepts. Many scholars have discussion in these aspects. The author of this article sets off discussion about the mutual dependence of two compnents e and 7/in the two dimensional discrete random variable （e 7/）. First we demonstrates three lemmas. Of the three lemmas, lemma 1 is introduced in general textbooks of probability theory, but the author also make a demonstration to lemma 1 for the conveinence of readers. The author of this article finds a necessary and sufficient condition of the independece of random variables by using the three lemmas.