代数不等式的概率证明方法

Probability Proof of Algebraic Inequalities

本文讨论了三种概率性质在代数不等式证明中的应用,阐述了如何针对不等式的特点构造随机事件和随机变量,运用概率强可加性、方差非负性、期望线性性质进行不等式证明,同时结合实例展示了证明过程和技巧.

This paper studies the use of three probability properties in the proof of algebraic inequalities, including strong additivity of probability, nonnegativity of variance and linear property of expectation. We expound on how to construct random events and random variables according to the characteristics of the inequalities. Several examples with the detailed proofs are provided to show our approaches.