概率在证明恒等式和不等式中的应用

概率在证明恒等式和不等式中的应用
 

摘要：概率论的思想已广泛应用于其它学科，用概率论中的方法解决其它学科中的1些问题是1个非常有趣的课题．本文利用概率论中方法证明恒等式和不等式，从中可看出它们之间的联系以及应用概率论方法解题的美妙之处．应用的基本思路是：根据所要解决的问题，首先构造1个适当的概率模型，然后应用概率中的已知结论解决所讨论的问题．如何构造适当的概率模型是解决问题的难点所在，也是关键所在．

关键词：随机变量；数学期望；方差；恒等式；不等式

The applications of probability theory in the
proofs of equalities and inequalities
 

Abstract: The thought of probability theory has already been applied to many other subjects extensively. It is very interesting to solve some problems in other subjects by using probability theory. In this paper, some methods in probability theory are used to prove several equalities and inequalities in Mathematics. By this, we can see the close relationship between them. It is also very valid to solve problems by using probability theory. Our method is as follows: according to the problem, we first construct their proper probability models, then use some known conclusions in probability theory to solve them. How to construct their probability models is the difficult point as well as the key point.
 
Key words: random variable; mathematical expectation; variance; equality; inequality