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本文分析了离散随机变量熵与方差及有关微分熵的某种关系，给出了离散随机变量熵的一个上界，改进了Ｔ．Ｍ．Ｃｏｖｅｒ与Ｊ．Ａ．Ｔｈｏｍａｓ关于离散熵的上界的已有结果［１］，并以图和表的方式举出一些实例加以比较。
In this paper, some relations between entropy and variance of discrete random variables and related differential entropy are analyzed. An upper bound of the entropy of discrete random variables is given, and T is improved. M. Cover and J. A. Thomas’s previous result on the upper bound of discrete entropy [1], and gives some examples by way of figures and tables for comparison.