类比教学法在“概率论与数理统计”课程中的应用——以连续型随机变量为例  

Application of Comparative Teaching Method for Probability Theory and Mathematical Statistics: Taking Continuous Random Variables as an Example

作　　者：钱欣洁 刘欢 QIAN Xin-jie;LIU Huan(College of Science,Jinling Institute of Tecnology,Nanjing,Jiangsu 211169,China)

机构地区：[1]金陵科技学院理学院,江苏南京211169

出　　处：《教育教学论坛》2023年第48期143-146,共4页Education And Teaching Forum

基　　金：2022年度金陵科技学院教研教改项目“基于达成度的通识课线上考核模式探索研究——以‘大学数学’课程为例”(JXGL202225);2021年度金陵科技学院孵化项目“Lienard系统中几个基本问题”(jit-fhxm-202116);2021年度金陵科技学院校级教育教改研究课题(JYJG202140)。

摘　　要：随机变量按取值形式可分为两类,离散型随机变量和非离散型随机变量。连续型随机变量作为非离散型随机变量中的一类,其相关内容是“概率论与数理统计”课程中的重难点。利用类比教学的方式,通过将连续型随机变量与学生熟悉的离散型随机变量对比,分别将连续型随机变量的概率密度、函数的分布、条件概率密度与离散型随机变量的分布律、函数的分布、条件分布律做类比,使学生更容易理解掌握连续型随机变量概率密度函数,函数的分布和条件概率密度。Random variables are divided into two categories according to the discrete situation of their values:discrete type and non-discrete type.Continuous random variable as a class of non-discrete random variable is one of the important and difficult mathematical research objects of probability theory and mathematical statistics course.In this paper,we draw an analogy between continuous and discrete random variables.More specifically,probability density function,distribution for function and conditional probability density function of continuous random variable were compared separately with distribution law,distribution for function and conditional distribution law of discrete random variable,to make it easier for students to understand and master the probability density function of continuous random variable and the distribution for function of continuous random variable.

关 键 词：类比教学 连续型随机变量 概率密度函数 随机变量函数的分布 条件概率密度 

分 类 号：G642.0[文化科学—高等教育学]