Probability & Statistics(概率论与数理统计)
定 价:25 元
丛书名:21世纪高等学校数学系列教材
- 作者:干晓蓉 著
- 出版时间:2009/1/1
- ISBN:9787307066922
- 出 版 社:武汉大学出版社
- 中图法分类:O21
- 页码:224
- 纸张:胶版纸
- 版次:1
- 开本:16K
- 字数:(单位:千字)
《Probability&Statistics(理工类本科生)》是作者在英国留学期间完成的自编教材基础上,结合国内双语课教学的实际而编写成的,是一本概率统计的入门教材。全书共分八章,内容包括概率公理、随机变量及其分布、多元随机变量、期望与方差、大数定律与中心极限定理、随机抽样、估计问题和假设检验。各章取材注重实际,力求叙述清晰易懂,书中配有适量的例题和习题,书末附有习题答案,便于教学和学生自学。
《Probability & Statistics(理工类本科生)》可以作为高等院校工科各专业、理科非数学专业以及管理与经济类等专业本科生的概率统计双语课程教材,也可以供相关科技人员参考。
数学是研究现实世界中数量关系和空间形式的科学,长期以来,人们在认识世界和改造世界的过程中,数学作为一种精确的语言和一个有力的工具,在人类文明的进步和发展中,甚至在文化的层面上,一直发挥着重要的作用,作为各门科学的重要基础,作为人类文明的重要支柱,数学科学在很多重要的领域中已起到关键性、甚至决定性的作用,数学在当代科技、文化、社会、经济和国防等诸多领域中的特殊地位是不可忽视的,发展数学科学,是推进我国科学研究和技术发展,保障我国在各个重要领域中可持续发展的战略需要.高等学校作为人才培养的摇篮和基地,对大学生的数学教育,是所有的专业教育和文化教育中非常基础、非常重要的一个方面,而教材建设是课程建设的重要内容,是教学思想与教学内容的重要载体,因此显得尤为重要。
为了提高高等学校数学课程教材建设水平,由武汉大学数学与统计学院与武汉大学出版社联合倡议,策划,组建21世纪高等学校数学课程系列教材编委会,在一定范围内,联合多所高校合作编写数学课程系列教材,为高等学校从事数学教学和科研的教师,特别是长期从事教学且具有丰富教学经验的广大教师搭建一个交流和编写数学教材的平台,通过该平台,联合编写教材,交流教学经验,确保教材的编写质量,同时提高教材的编写与出版速度,有利于教材的不断更新,极力打造精品教材。
本着上述指导思想,我们组织编撰出版了这套21世纪高等学校数学课程系列教材,旨在提高高等学校数学课程的教育质量和教材建设水平。
参加21世纪高等学校数学课程系列教材编委会的高校有:武汉大学、华中科技大学、云南大学、云南民族大学、云南师范大学、昆明理工大学、武汉理工大学、湖南师范大学、重庆三峡学院、襄樊学院、华中农业大学、福州大学、长江大学、咸宁学院、中国地质大学、孝感学院、湖北第二师范学院、武汉工业学院、武汉科技学院,武汉科技大学、仰恩大学(福建泉州)、华中师范大学、湖北工业大学等20余所院校。
高等学校数学课程系列教材涵盖面很广,为了便于区分,我们约定在封首上以汉语拼音首写字母缩写注明教材类别,如:数学类本科生教材,注明:SB;理工类本科生教材,注明:LGB;文科与经济类教材,注明:WJ;理工类硕士生教材,注明:LGs,如此等等,以便于读者区分。
1 The Axioms of Probability
1.1 Experiments
1.2 Sample Spaces and Events
1.3 Frequency and Probability
1.4 Equally Likely Outcomes
1.5 Conditional Probability
1.6 Independence
Exercise 1
2 Random Variables and Their Distributions
2.1 Random Variables
2.2 Discrete Random Variables
2.3 Cumulative Distribution Functions
2.4 Continuous Random Variables
2.5 Functions of Random Variables
Exercise 2
3 Multivariate Random Variables
3.1 Two——Dimensional Random Variables
3.2 Marginal Distributions
3.3 Conditional Distributions
3.4 Independence
3.5 Distribution of Special Functions
Exercise 3
4 The Mean and Variance
4.1 Expectations of random variables
4.2 Variances of random variables
4.3 Covariance & Correlation
4.4 Miment and Covariance Matrix
Exercise
5 The Law of Large Numbers and the Central Limit Theorem
5.1 Chebyshevs Inequality
5.2 Law of Large numbers
5.3 The Central Limit Theorem
Exercise 5
6 Random Sampling
6.1 Random Sampling
6.1.1 Populations and Samples
6.1.2 Random Sample
6.2 Some Important Statistics
6.2.1 The Sample Mean and the Sample Variance
6.2.2 The Sample Moments
6.3 Sampling Distributions
6.3.1 The Chi-Square distribution
6.3.2 t-Distribution
6.3.3 F-Distribution
6.3.4 Quantile of Order tt
6.3.5 Sampling Distributions of the Sample Mean and the Sample Variance
Exercise 6
7 Estimation Problems
7.1 Introduction
7.2 Point Estimation
7.2.1 The Method of Moments
7.2.2 The Method of Maximum Likelihood
7.3 The Particular Properties of Estimators
7.3.1 Unbiased Estimators
7.3.2 Efficiency
7.3.3 Consistency
7.4 Interval Estimation
7.4.1 The Estimation of Mean
7.4.2 The Estimation of Variance
Exercise 7
8 Hypothesis Testing
8.1 Introduction
8.2 Tests Concerning Means
8.2.1 One Normal Population
8.2.2 To Normal Populations
8.3 Tests Concerning Variances
8.3.1 One Normal Population
8.3.2 Two Normal Populations
8.4 The Relationship Between Hypothesis Testing and Confidence Intervals
8.5 One Sample: Thex2 Goodness of Fit Test
Exercise 8
Appendix A Some Important Distributions
Appendix B Statistical Tables
Appendix C Answer To Exercise
Appendix D 中英文对照表
Bibliography
1 The Axioms of Probability
1.1 Experiments
An experiment is any action or process that generates observations. Although the word experiment generally suggests a planned or carefully controlled laboratory testing situation, we use it here in a much wider sense. Thus, experiments that may be of interest include tossing a coin once or several times, selecting a card or cards from a deck, weighing a loaf of bread, or measuring the compressive strengths of different steel beam, etc. The experiments may be quite simple or they may be composite. In any case, the result of an experiment is a single outcome from a basic set of such potential outcomes.
Probability theory deals with situations in which there is a degree of randomness or chance in the outcome of some experiment. We are specifically concerned with experiments that can be repeated under identical circumstances. In such a situation it is desirable to know the chance of such an outcome of occurring.Here are a few illustrative examples:(El) Choose two people at random from a group of five people.
What is the probability that a particular person is in the selected pair?
(E2) A coin is tossed three times. What is the probability that exactly two heads are obtained?
(E3) Choose a positive integer n = ( 1, 2, 3," ) by means of the following experiment. Toss a fair coin repeatedly until you get head and let n be the number of tosses up to and include the first toss resulting in head.What is the probability that n is an odd number?