全概率公式的两点注记  

Two Notes on Total Probability Theorem

作　　者：李佳[1] 邓有莲[2] LI Jia;DENG Youlian(School of Computer and Information Engineering,Jiangxi Normal University,Nanchang 330022,China;School of Mathematics and Information Science,Jiangxi Normal University,Nanchang 330022,China)

机构地区：[1]江西师范大学计算机信息工程学院,南昌330022 [2]江西师范大学数学与信息科学学院,南昌330022

出　　处：《成都师范学院学报》2018年第11期97-101,共5页Journal of Chengdu Normal University

基　　金：江西省教育厅科学技术研究项目"多维计算机化自适应测验新选题算法研究"(GJJ170212);江西师范大学教改课题资助项目"探究式教学方法在<离散数学>中的应用研究"(JXSDJG1767)

摘　　要：全概率公式和贝叶斯公式是《概率统计》中两个重要的概率计算公式,它们的使用条件不一定需要在样本空间划分的前提条件下,可以放宽到两两互不相容正概率事件的前提下;全概率公式的解题思路——分解法在《概率统计》离散型随机变量期望和方差的求解过程中也有着广泛的应用.文章介绍的这两点注记不仅是对现有《概率统计》教材内容的有益补充,也有利于激发学生的学习兴趣、加深学生对全概率公式和贝叶斯公式的全面理解和掌握。Total probability theorem and Bayes'rule are two important probability calculation theorems in Probability Statistics.The condition of using total probability theorem and Bayes'rule can be relaxed under the presupposition of mutually exclusive events with normal probability but not necessarily under the presupposition of sample space partition.The decomposition method,the idea of solving the problem in total probability theorem,can be widely applied in solving expected value and variance of discrete random variables in Probability Statistics.The two notes are beneficial to the supplement for the content of Probability Statistics,the stimulation of students'learning interest and the enhancement of students'comprehension and mastering of total probability theorem and Bayes'rule.

关 键 词：全概率公式 分解法 期望 方差 

分 类 号：G642[文化科学—高等教育学] O211.9[文化科学—教育学]