本文用概率方法证明了关于两个相异的正数的几何平均、对数平均、指数平均和算术平均的不等式关系。
In this paper, we prove the inequality relations of arithemetric mean, logarithmic mean, exponential mean and geometric mean for two positive numbers by using probabilistic method.
得出伦德伯格不等式和最终破产概率公式。
Then the Lundberg inequality and the formula of the ruin probability are obtained.
文中通过几个不等式的证明阐明了常用的概率思想方法。
In this paper, we illustrate probability thinking method through several inequalities proof.
本文列举了利用概率论的思想方法证明不等式的六种基本方法。
This article enumerates six fundamental methods of using the method of thinking of probability to prove the inequality.
文中在分析数学的几个重要不等式的证明之中引进了概率方法，取得较好的效果。
Better results are got during the course of the proofs of several inequalities in analysis mathematics by using probabilistic method.
应用鞅论的方法，得出破产概率的一个不等式。
By using the method of Martingale, we get the inequality for the ultimately ruin probability.
概率论是数学的一个重要分支，不等式的证法是多种多样的。
The probability is one of the most important branches of mathematics There are various methods of proving the inequality.
概率论是数学的一个重要分支，不等式的证法是多种多样的。
The probability is one of the most important branches of mathematics There are various methods of proving the inequality.
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