摘要:概率论是数学的一个分支，它研究随机现象的数量规律，被广泛地应用，几乎遍及所有的科学领域，通过对某些事件概率的探究，可以帮助人们了解、发现规律，揭示事件的秘密，从而做出合理的判断和预测。因此，概率论就成为我们认识客观世界的有效工具。概率不等式是概率论与数理统计中的重要知识点，其中包含的马尔可夫不等式、切比雪夫不等式等在现实的生活中有一定的涉及和运用。认识并了解概率不等式的证明及应用对解决生活中的大量随机现象平均结果的稳定性有重要意义，也为更好地解决生活中的大量随机现象提供便捷的方法。

关键词：切比雪夫不等式； 矩估计不等式； 概率不等式的应用

Abstract:Probability theory is a branch of mathematics. It studies the number of laws of random phenomena, and it has been widely applied in virtually all fields of science. Exploring the probability of certain events, helps people understand, discover the laws, and reveal the secrets of the incident, then make reasonable judgments and projections. Therefore, Probability has become an effective tool to help us understand the objective world. Inequality is the important point in the “Probability probability and Statistics”, which contains the Markov inequality, Chebyshev inequality, In real life, and involving the use of certain. Awareness and understanding of proof of the probability inequalities to solve a large number of random phenomena in the life of the average importance of the stability of the results in real life is very important, also to better solution for a large number of random phenomena in life provides a convenient method.

Keywords: Chebyshev-inequality  Moment estimation inequalities  Application of probability inequalities