二维随机变量独立性分析及教学案例设计  

Independence Analysis of Two-dimensional Random Variables and its Teaching Case Design

作　　者：贺方超[1] 陈金玉 汪慧 HE Fangchao;CHEN Jinyu;WANG Hui(School of Science,Hubei University of Technology,Wuhan,Hubei 430068)

机构地区：[1]湖北工业大学理学院,湖北武汉430068

出　　处：《科教导刊》2022年第27期136-139,共4页The Guide Of Science & Education

基　　金：湖北工业大学教学研究项目(NO.校2018028);湖北省教育厅教学研究课题(NO.省2018327)

摘　　要：随机变量独立性分析是本科概率统计课程中的重要知识点。本文首先回顾了二维随机变量独立性的三个性质,接着通过对一道课堂例题结果的观察与思考,从矩阵及向量线性相关的角度给出了二维离散型随机变量相互独立条件下的两个定理,并进一步将二维随机变量独立性的性质推广到连续型的情形。最后,为使该性质得到更好的理解和运用,将其融入实际问题的求解中,以激发学生的数学思维,从整体掌握三个定理的应用。The independence analysis of random variables is an important knowledge point in undergraduate probability and statistics course.This paper first reviews the three properties of the independence of two-dimensional random variables.And then based on the observation and reflection on the results of a classroom teaching case,this paper gives two theorems under the condition that two-dimensional discrete random variables are independent of each other from the perspective of linear correlation between matrix and vector.Furthermore,the property of the independence of two-dimensional random variables is extended to the continuous case.Finally,the independence property is integrated into the solution of practical problems for better understanding and application.This will stimulate students’mathematical thinking and master the application of the three theorems as a whole.

关 键 词：随机变量 独立 线性相关 边缘分布律 边缘概率密度 

分 类 号：G642[文化科学—高等教育学] O211.5-4[文化科学—教育学]