随机变量独立性的判定与运用

The judgment and application of the independence of random variables

主要研究了二维离散型随机变量和二维连续型随机变量的独立性问题.对于二维离散型随机变量,先从简单例子分析得到判定定理,然后从线性代数的角度予以考虑,分别用矩阵的初等变换和秩的相关概念对其进行了证明.对于二维连续型随机变量,介绍了一个比较直观的定理;同时,对其应用进行了举例说明.

The independence of random variable is the important concept of probability theory. This paper studies the independence of two com- mon random variables：two-dimensional discrete random variables and two-dimensional continuous randow variables. For two-dimensional dis- crete random variables, the conclusion was firstly obtained by simple examples, then illustrated from the aspect of linear algebra, and later explained form the elementary transformation of Matrix and the relevant concepts of Rank. For two-dimensional continuous random variables, its application was also illustrated with examples while introducing a theorem explicitly.