求随机变量期望和方差的微分恒等式法  

Method of Differentiating Identities for Calculating Expectation and Variance of Random Variables

作　　者：王福昌[1] 张丽娟[1] WANG Fuchang and ZHANG Lijuan(Department of Basic Courses,Institute of Disaster Prevention,Sanhe 065201,China)

机构地区：[1]防灾科技学院基础部,河北三河065201

出　　处：《高等数学研究》2024年第4期23-26,28,共5页Studies in College Mathematics

基　　金：防灾科技学院教育研究与教学改革项目(JY2022A03)。

摘　　要：首先介绍微分恒等式法,然后利用这种方求出了二项分布、泊松分布、几何分布、负二项分布、Gamma分布和正态分布等常见随机变量的期望和方差,说明了方法的有效性.The method of differential identities is introduced and used to find the expectations and variances of binomial distribution,Poisson distribution,geometric distribution,negative binomial distribution,gamma distribution and normal distribution.The effectiveness of the method is evidenced.

关 键 词：微分恒等式 期望 方差 

分 类 号：O211[理学—概率论与数理统计]