Markov不等式和Chebyshev不等式在概率论中的应用  

Application of Markov's inequality and Chebyshev's inequality to the probability theory

作　　者：张海芳 

机构地区：[1]滇西科技师范学院数理系,云南临沧677099

出　　处：《滇西科技师范学院学报》2015年第4期121-124,共4页Journal of West Yunnan University

摘　　要：概率论是从数量侧面研究随机现象规律性的数学学科,它有自己独特的概念和方法,内容丰富,应用广泛。不等式是数学中一项非常重要的内容。关于概率论和不等式的研究已空前活跃,当然也得出了很多经典的结论。其中应用概率论证明不等式,已成为不等式证明中不可或缺的方法。另一方面不等式在概率的各个方面也是至关重要的。其中Markov不等式和Chebyshev不等式就是概率论中两个最基本的不等式。文章从这两个不等式出发,证明了概率论中的几个理论问题,得出了概率估值计算的几个方法,最后给出了一个简单的举例应用。Probability theory is the branch of mathematics concerned with probability, the analysis of random phenomena, and is widely applicable due to its unique concepts and methods. Inequality is a key element in mathematics. The researches on probability theory and inequality have obtained rich achievements. The application of probability theory to the solutions of the problems of inequality is popular, or vice versa. Markov＇s inequality and Chebyshev＇s inequality are two most popular inequalities in probability theory. Using the two inequalities to study several theoretical problems in probability theory, this paper has obtained several methods for probability estimation. It finally gives a case application.

关 键 词：Markov不等式 CHEBYSHEV不等式 概率 

分 类 号：O211[理学—概率论与数理统计]