几类概率问题求解中样本空间的选取
The Choosing for Sample Space in Solving Several Kinds of Probability Problems
摘要:
样本空间是概率论的基本的概念之一，恰当选取样本空间是求解很多概率问题的关键。本文针对古典概率、几何概率、条件概率、随机变量及其分布等问题中遇到的有关样本空间的选择问题，给出了样本空间的选取原则，全面阐明了恰当选取样本空间在求解相关概率问题中的重要性，最后，分析了样本空间的形态与概率方法的一致性问题。
Abstract:
Sample space is one of the basic concepts of probability theory, and appropriate choosing for the sample space is the key to solving many probability problems. This paper mainly deals with the problems of the choosing for sample space in classical probability, geometric probability, conditional probability, random variables and its distribution, gives the principle of the choosing for sample space, illustrates the importance of the choosing for sample space in solving some related probability problems, and analyzes the consistency of the form for sample space and the method of the probability problems.
参考文献
|
[1]
|
程海奎, 章建跃. 用样本空间刻画随机现象定义随机事件的概率发展学生的随机观念[J]. 数学通报, 2021, 60(5): 1-9.
|
|
[2]
|
邱瑶. “样本点、样本空间和随机事件的表达”教学设计[J]. 中国数学教育, 2021(4): 50-54.
|
|
[3]
|
谭雪莹, 胡典顺. 概率与统计的知识理解之样本空间[J]. 数学通报, 2021(18): 1-3.
|
|
[4]
|
郭华. 恰当选取样本空间, 简化古典概率计算[J]. 高等数学研究, 2000(3): 35-36.
|
|
[5]
|
兰旺森. 概率论教学中与样本空间有关的几个问题[J]. 高师理科学刊, 2017, 37(11): 50-52.
|
|
[6]
|
石亮. 一道几何概型题的探究、变式及引申[J]. 数学教学通讯, 2009(24): 60-61.
|
|
[7]
|
张德然, 何鹏光. 关于古典概率计算中样本空间的构造及优化[J]. 阜阳师范学院学报(自然科学版), 2005, 22(2): 71-74.
|
|
[8]
|
郑玉仙. 缩减样本空间在条件概率计算中的应用[J]. 浙江水利水电专科学校报, 2006, 18(1): 57-58.
|
|
[9]
|
杨洋, 张燕, 居艳. 概率解题中样本空间的选择[J]. 高等数学研究, 2007, 10(1): 96-98.
|
|
[10]
|
茆诗松. 概率论与数理统计教程[M]. 北京: 高等教育出版社, 2004: 48.
|
|
[11]
|
Vos, P. and Anaya-Izquierdo, K. (2014) Using Geometry to Select One Dimensional Exponential Families That Are Monotone Likelihood Ratio in the Sample Space, Are Weakly Unimodal and Can Be Parametrized by a Measure of Central Tendency. Entropy, 16, 4088-4100. [Google Scholar] [CrossRef]
|
|
[12]
|
王展青, 王传廷, 张富铭, 赵―鹏. 基于有效候选集的支持向量机样本选择方法[J]. 计算机工程与应用, 2008, 44(23): 214-216.
|