数学期望不等式的应用  

Application of Mathematical Expectation Inequality

作　　者：刘敬[1] 

机构地区：[1]福建经济管理干部学院信息管理系,福建福州350002

出　　处：《河北北方学院学报（自然科学版）》2008年第4期6-7,共2页Journal of Hebei North University:Natural Science Edition

摘　　要：目的利用微积分理论证明不等式的方法很多,探讨用概率理论证明不等式的方法.方法首先构造一个概率密度函数,再利用数学期望不等式E(η)2≥E2(η)证明一个积分不等式.结果由该积分不等式推出若干数学不等式.结论利用概率方法可以证明某些不等式,且方法简单,关键是构造恰当的概率密度函数,再利用概率中有关不等式的性质.Objective There are a lot of methods used to prove inequality by using differential calculus theory. This paper is about the methods of using probailitic theory to prove inequality. Methods Firstly structuring the probalilistic density function, then using mathematical expectation inequality E （η^2）≥E^2 （η） to prove integral inequality. Results Using integral inequality some mathematical inequalities are proved. Conclusion Using probalilistic methods some mathematical inequalities can be proved easily. The key point is to structure a proper probalilistic density function before using the qualities of inequalities in probability.

关 键 词：随机变量 数学期望 密度函数 

分 类 号：O175[理学—数学]