This book includes the probability of events, discrete random variables and their distribution, continuous random variables and their distribution, digital characteristics of random variables, law of large numbers and central limit theorem, sampling distribution, parameter estimation and hypothesis testing.All of the authors of this book have the background of visiting British and American university. The writing language is easy to understand, and the content has moderate difficulty.This book can be used for the teaching of probability and statistics courses of Sino-foreign cooperation projects and foreign student programs in universities of science and engineering non-mathematics majors, as well as bilingual teaching of probability and statistics.
本书内容包括事件的概率、离散型随机变量及其分布、连续型随机变量及其分布、随机变量的数字特征、大数定律与中心极限定理、抽样分布、参数估计和假设检验。本书编著者均有英美访学背景，英文语言简单易懂，写作简约，内容难易适中，便于学习。本书可供理工科大学（非数学专业）中外合作办学项目和留学生项目的概率统计课程教学使用，也可供概率统计双语教学使用。This book includes the probability of events, discrete random variables and their distribution, continuous random variables and their distribution, digital characteristics of random variables, law of large numbers and central limit theorem, sampling distribution, parameter estimation and hypothesis testing.All of the authors of this book have the background of visiting British and American university. The writing language is easy to understand, and the content has moderate difficulty.This book can be used for the teaching of probability and statistics courses of Sino-foreign cooperation projects and foreign student programs in universities of science and engineering non-mathematics majors, as well as bilingual teaching of probability and statistics.
本书内容包括事件的概率、离散型随机变量及其分布、连续型随机变量及其分布、随机变量的数字特征、大数定律与中心极限定理、抽样分布、参数估计和假设检验。本书编著者均有英美访学背景，英文语言简单易懂，写作简约，内容难易适中，便于学习。本书可供理工科大学（非数学专业）中外合作办学项目和留学生项目的概率统计课程教学使用，也可供概率统计双语教学使用。
目錄：
Chapter 1Introduction001
1.1The Origin of Probability Theory and Mathematical Statistics001
1.2Random Phenomena and Random Trials002
1.3Statistical Regularity of Random Phenomena003
1.4Some Important Applications of Probability and Statistics004
Chapter 2Basic Probability006
2.1Set Theory006
2.1.1Sets,Elements,and Subsets006
2.1.2Set Operation：Union,Intersection,Complement and Set Differences,Exclusive and Opposite008
2.1.3Experiments,Sample Spaces,and Events010
2.2Set Functions011
2.2.1Boolean Algebras011
2.2.2Measures013
2.2.3Examples of Measures013
2.2.4Measures on Partitions of Sets014
2.3Probability as Measure014
2.3.1Properties of Probability015
2.4Assigning Probabilities016
2.4.1Classical Probability Based on Symmetry016
2.4.2Counting Methods for Classical Probability：Permutations and Combinations017
2.4.3Estimated ProbabilityRelative Frequency019
2.4.4Subjective Probabilities020
2.5Conditional Probability021
2.5.1Independence022
2.5.2The Law of Total Probability023
2.5.3Bayes Theorem024
Exercises025
Chapter 3Discrete Random Variables028
3.1Random Variables028
3.2Probability Distributions for Discrete Random Variables030
3.2.1Probability Mass Function PMF030
3.2.2Cumulative Distribution FunctionCDF031
3.2.3Derived Distributions of Discrete Random Variables034
3.3Some Important Discrete Probability Distributions035
3.3.1The Bernoulli Distribution035
3.3.2The Binomial Distribution036
3.3.3Hypergeometric Distributions037
3.3.4The Poisson Distribution040
3.4Multiple Discrete Random Variables042
3.4.1Joint Distribution 042
3.4.2Marginal Distribution 044
3.4.3Conditional Distribution045
3.4.4Independence of Discrete Random Variables048
3.4.5Derived Distributions of Multiple Discrete Random Variables049
Exercises049
Chapter 4Continuous Random Variables054
4.1Continuous Random Variable054
4.1.1Continuous Probability Distribution 054
4.1.2Some Important Continuous Distribution059
4.2Multiple Continuous Random Variables066
4.2.1Joint Distribution066
4.2.2Marginal Distribution067
4.2.3Conditional Distribution069
4.2.4Independence of Continuous Random Variables070
4.3Derived Distributions of Continuous Variable071
Exercises076
Chapter 5Numerical Characteristics of Random Variables080
5.1Expectation080
5.1.1Average & Expectation080
5.1.2Expectations for Functions of Random Variables 082
5.1.3Moments of the Random Variable085
5.2Variance 086
5.2.1Variance & Standard Deviation086
5.2.2Expectations & Variance for Several Common Distributions091
5.3Covariance and Correlation Coefficient094
5.3.1Covariance and Correlation Coefficient094
5.3.2The Essence of Covariance and Correlation Coefficient097
Exercises100
Chapter 6Sums of Random Variables105
6.1Sums of Independent and Identically Distributed Random Variables105
6.2Laws of Large Numbers107
6.2.1Chebyshevs Inequality107
6.2.2The Weak Law of Large Numbers107
6.3The Central Limit Theorem CLT108
6.3.1Example：Sums of Exponential Random Variables109
6.3.2Example：Sums of Bernoulli Random Variables，and the Normal Approximation to the Binomial Distribution109
Exercises111
Chapter 7Random Samples and Sampling Distributions113
7.1Random Sampling113
7.2Some Important Statistics115
7.2.1Location Measures of a Sample116
7.2.2Variability Measures of a Sample117
7.3Sampling Distributions119
7.4Some Important Sampling Distribution120
7.4.1Chi-square Distribution120
7.4.2Students Distributiont-Distribution124
7.4.3F-distribution128
Exercises131
Chapter 8Estimation and Uncertainty133
8.1Point Estimation133
8.1.1Some General Concepts of Point Estimation133
8.1.2Selection Criteria of Point Estimators135
8.2Method of Point Estimation142
8.2.1Method of Moments142
8.2.2Method of Maximum Likelihood144
8.3Interval Estimation149
8.3.1Basic Concepts of Confidence Intervals149
8.3.2Confidence Intervals for Parameters of a Normal Population151
8.3.3Confidence Intervals for the Difference of the Sample Means 1-2155
8.4Confidence Interval for a Population Proportion p159
Exercises160
Chapter 9Hypothesis Testing164
9.1Basic Concepts and Principles of Hypothesis Testing164
9.1.1Hypothesis and Test Statistic164
9.1.2Errors in Hypothesis Testing167
9.2Hypotheses on a Single Normal Population168
9.2.1Hypothesis Concerning a Single Mean169
9.2.2Hypothesis Concerning a Single Variance171
9.3Two-Sample Tests of Hypotheses 174
9.3.1Tests on Two Means174
9.3.2Tests on Two Variances177
Exercises179
Chapter 10Application of R in Probability and Statistics182
10.1R Software Overview182
10.1.1Download and Installation of R Software182
10.1.2Using R as a Calculator183
10.1.3Defining and Using Variables184
10.1.4Vectors184
10.1.5Plotting Graphs185
10.2R in Solving Probability and Statistical Problems187
10.2.1Probability Calculation187
10.2.2Plotting Statistical Graphs188
10.2.3Descriptive Statistics188
10.2.4Estimation in R190
10.2.5Testing Hypothesis on Mean and Variance of Normal Population195
Appendix Statistical Tables198
Table 1Poisson Distribution198
Table 2Standard Normal Distribution Function200
Table 3Values of 2201
Table 4Values of t203
Table 5Values of F204
References210
內容試閱：
Preface
Probability and statistics are a subject that studies the regularity of random phenomena.Because of the universality of random phenomena, the methods of probability theory and mathematical statistics almost infiltrate into the fields of natural science, technical science and economic management.
As an introduction to probability and statistics, in order to convey the importance and practicability of the course to the readers, this book first gives a brief introduction in Chapter 1 to its development history, research objects and applications in various fields of natural science and national economy.Then the part of probability theory Chapter 2 to Chapter 6 and the part of statistics Chapter 7 to Chapter 9 are discussed respectively.Probability theory, as the theoretical basis, mainly describes the probability of events, random variables and their distribution, numerical characteristics, the law of large numbers and the central limit theorem.The main contents of mathematical statistics include sampling distribution, parameter estimation and hypothesis test.The last part Chapter 10 introduces how to use R software to solve the related calculation problems in probability and statistics.
In the process of writing this book, we strive to make the content easy to understand.We fully combine the characteristics of probability and statistics textbooks at home and abroad, weaken mathematical derivation in narration, and emphasize intuitive understanding.The selection of examples and exercises is combined with practice as far as possible, and we pay attention to the application of probability and statistics theories and methods in various fields.In addition, the discussion of this book tries to be in line with the thinking habits of the readers. The professional nouns in each chapter are annotated in the form of footnotes, which is convenient for readers to read and find.
In this volume, Chapter 1 is written by Shi Qingsheng, Chapter 2 and Chapter 6 are written by Ma Shujian, Chapter 3, Chapter 4 and Chapter 5 are written by Shen Min, Chapter 7, Chapter 8, Chapter 9, Chapter 10 and Appendix are written by Chen Jianli.All the chapters are checked and revised by Chen Jianli.The overall framework of this book is determined under the guidance of Professor Shi Qingsheng, and he gives us a lot of valuable suggestions in the process of writing.
Due to the limit of our ability, there are inevitably shortcomings and mistakes in the book.We would appreciate any constructive criticisms and corrections from readers.
Chen Jianli, Shen Min, Ma Shujian, Shi Qingsheng
2020.6
前言
概率论与数理统计是研究随机现象规律性的一门学科。由于随机现象存在的普遍性，使得概率论与数理统计的方法几乎渗入到自然科学、技术科学以及经济管理等各领域中。
作为概率论与数理统计的入门教材，本书的编写首先通过第一章对它的发展历史、研究对象以及在自然科学、国民经济各领域中的应用进行简要介绍，以期向读者传递该课程的重要性及实用性。然后分别对概率论部分（第二章到第六章）和数理统计部分（第七章到第九章）展开论述。概率论部分作为理论基础部分，主要讲述事件的概率、随机变量及其分布、数字特征以及大数定律与中心极限定理。数理统计部分的主要内容包括抽样分布、参数估计和假设检验。最后部分（第十章）介绍了如何用R软件解决概率统计中的相关计算问题。
本书在编写过程中，努力做到通俗易懂，简详得当。充分结合国内外概率统计教材的特点，弱化数学推导，加强直观理解。例题和习题尽量联系实际，注重体现概率统计理论、方法在各个领域的应用。另外，本书的论述尽量做到符合读者的思维习惯，并对每一章中出现的专业名词以脚注的形式进行中文注释，便于读者阅读和查找。
参加本书编写的有施庆生（第一章）、马树建（第二、六章）、申敏（第三~五章）、陈建丽（第七~十章和附录），最后由陈建丽负责全书的统稿和定稿。施庆生教授指导确定了本书整体编写框架，并在编写过程中给出了许多宝贵意见。
本书的编写获得江苏省第二批中外合作办学高水平示范性建设工程项目培育点：南京工业大学与英国谢菲尔德大学合作举办数学与应用数学（金融数学）专业本科教育项目苏教办外［2017］14号经费支持。
由于编者水平所限，书中难免存在错误和不足之处，敬请读者批评指正。
陈建丽、申敏、马树建、施庆生
2020.6
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