巧用概率方法证明不等式  

Proving inequalities by using probability method

作　　者：贾朝勇[1] 潘玉荣[1] 

机构地区：[1]蚌埠学院数理系,安徽蚌埠233030

出　　处：《佛山科学技术学院学报（自然科学版）》2016年第2期12-16,共5页Journal of Foshan University(Natural Science Edition)

基　　金：安徽省高等学校优秀青年教师人才科研资助项目(2012SQRL215);蚌埠学院教研项目(2013jyxm04)

摘　　要：通过实例展示了如何巧妙借助概率论的思想方法来证明不等式,其关键点是:根据待证不等式具体形式去构造适当概率模型,再应用随机事件的运算、概率的相关性质、随机变量函数的数学期望的定义、切比雪夫不等式或马尔克夫不等式等证明不等式。此种证明方法不仅为证明不等式提供了一种新思路,而且还沟通了不同数学学科之间的联系。This paper shows how to use the ideas and methods of probability theory to prove inequality through theexamples cited to readers, the key point is according to the specific form of inequality to construct the appropriateprobability model, then using computation of random events, and the related properties of probability, thedefinition of mathematical expectation of random variable function, Chebyshev inequality or Markov inequality toprove inequality. The proof method provides a new idea for proving inequality, and also communicates theconnection between different mathematics subjects.

关 键 词：不等式 概率模型 随机变量 切比雪夫不等式 马尔克夫不等式 

分 类 号：O178[理学—数学]