中文摘要：

从两个随机事件的独立性出发,引入两个随机变量的独立性与相关性的概念,给出独立性与相关性的一些常见判别方法及注记,通过实例说明使用密度函数判别独立性有出错的可能,进而给出使用密度函数判别独立性的一个充要条件,以避免判别错误的发生。最后用一些实例说明独立性与相关性在实际生活中的应用。

英文摘要：

The concepts of independence and correlation of two random variables are introduced from the independence of two random events. Further we give some notes and discriminated methods for judging independence and correlation. By using the density function in general teaching material for judging independence is easy to make mistakes, and we analyze the situation of the mistakes which are easy to make by an example. To solve this problem, we in this paper, give a necessary and sufficient condition for judging the independence via the density function, which can avoid this mistake. At last, some real examples are taken to illustrate the applications of independence and correlation in life.