由毛纲源、徐丽莉编著的《概率论与数理统计(英文版普通高等院校数学精品教材)》是概率论与数理统计教材，采用全英文编写，是作者几十年来在教学一线教学工作的经验总结，在编写过程中参考了国外优秀的英语微积分教材，摒弃不适合中国学生使用的一些内容。本书的主要包括随机事件与概率、古典概率的计算、一维随机变量及概率分布、二维随机变量及其分布、随机变量的数字特征、大数定律和中心极限定理、样本及抽样分布、参数估计等内容。本书在定稿之前已在多个学校作为校本教材试用，而且均得到了师生的好评。 本书适合中外合作办学的国际教育学生，帮助他们较快地适应全英文的学习内容和教学环境，完成与国外大学学习的衔接。同时，也可以作为大学数学双语教学教师和准备出国留学深造学子的参考书。

Probability and statistics is a basic course of statistical regularity of random phenomena,whichfocuses on the interpretations, methods and theories in probability and statistics as well as presen-ting the specific application in all fields according to their characteristics.

Ideas and concepts are shown in this textbook with plenty of examples in order to make thecourse structure easier to understand. You are supposed to comprehend and understand the basicconcepts of probability and mathematical statistics somehow by reading this book, knowing how todeal with random experiments as well. It also trains readers to use the methods to analyze and solveactual problems,and lays a solid basis of statistics for the future study of other related advancedcourses.

《概率论与数理统计(英文版普通高等院校数学精品教材)》由毛纲源、徐丽莉编著。

Chapter 1 Introduction to Probability

 1.1 Sets and Set Operations

 1.2 Random Experiments

 1.3 Sample Space

 1.4 Events (Random Events)

1.4.1 The concept of events (random events)

1.4.2 Relations among events

1.4.3 Operations of events

 1.5 Relative Frequency

 Exercise 1

Chapter 2 Finite Sample Spaces

 2.1 Classical Probability Model

2.1.1 Finite sample spaces

2.1.2 Equally likely outcomes

2.1.3 Classical probability model or equally likely probability model

2.1.4 Counting methods

 2.2 Basic Properties of Probability

 Exercise 2

Chapter 3 Conditional Probability and Independence

 3.1 Conditional Probability

 3.2 Product Rule (Multiplication Rule)

 3.3 Total Probability Law

 3.4 Bayes' Theorem

 3.5 Independent Events

3.5.1 Independence of two events

3.5.2 Independence of several events

 Exercise 3

Chapter 4 Random Variables and Distributions

 4.1 Definition of Random Variable

 4.2 Discrete Random Variable

4.2.1 Probability distribution of discrete random variables

4.2.2 Some commonly used discrete probability distributions

 4.3 Cumulative Distribution Function

4.3.1 Finding the cumulative distribution function of discrete variable

4.3.2 Determining probability by the distribution function

4.3.3 Finding the probability function of a random variable with cumulative distribution function

 4.4 Continuous Random Variable

4.4.1 Continuous random variable and probability density function

4.4.2 Some continuous probability distributions

 4.5 Finding the Distribution of Random Variable Function

4.5.1 Finding the probability distribution of discrete random variable function

4.5.2 Finding the p. d. f. of the function Y=g(X) ,where y=g(x) is continuous monotonic function

4.5.3 Finding the p. d. f. of the function Y=g(X) where X is a continuous random variable

4.5.4 Finding the distribution of the function Y=g(X) where X is a continuous random variable

 Exercise 4

Chapter 5 Two-dimensional Random Variable

 5.1 Concept of Joint Probability Distribution

5.1.1 Joint probability distribution for two discrete random variables

5.1.2 Marginal distribution of discrete random variable

5.1.3 Joint probability distribution function for two continuous random variables

5.1.4 Marginal probability density function and conditional probability density

5.1.5 The joint P.d.f.for two random variables

 5.2 Conditional Distribution

 5.3 Two Commonly Useful Distributions

5.3.1 TWO—dimensional uniform distribution

5.3.2 Bivariate normal distribution

 5.4 Independence of Two Random Variables

 Exercise 5

Chapter 6 Numerical Characteristics of Random Variables

 6.1 Expectation of Random Variable

6.1.1 Expectation of discrete distribution

6.1.2 Expectation of continuous random variable

6.1.3 The expectation of function

6.1.4 Properties of expectation

 6.2 Variance of Random Variable

6.2.1 Definition of the variance and the standard deviation

6.2.2 Properties of the variance of random variable

6.2.3 The expectation and variance of special probability distribution

 6.3 Covariance and Correlation

6.3.1 Covariance

6.3.2 Correlation coefficient

 6.4 Moments and Covariance Matrix

 Exercise 6

Chapter 7 Law of Large Number and Central Limit Theorem

 7.1 Chebyshev’S Inequality

 7.2 Law of Large Number

 7.3 Central Limit Theorem

 Exercise 7

Chapter 8 Basic Concept in Mathematical Statistics Introduction

 8.1 Random Sampling

8.1.1 Population and sample

8.1.2 Random sample

8.1.3 Distribution of random sample

 8.2 Statistics

 8.3 Sampling Distribution

8.3.1 The chi-square distribution

8.3.2 The t-distribution

8.3.3 The F-distribution

 8.4 Sampling Distribution Related to Sample Mean or (and)Sample Variance from Normal Population

8.4.1 Sampling distribution related to sample mean or (and)sample variance from one normal population

8.4.2 Sampling distribution related to sample mean of (and)sample variance from two normal populations

Exercise 8

Chapter 9 Parameter Estimation

 9.1 Point Estimation

 9.2 The Particular Properties of Estimators

9.2.1 Unbiasedness

9.2.2 Validity

9.2.3 Consistency

 9.3 Moment Estimation and Maximum Likelihood Estimation

9.3.1 Moment estimation

9.3.2 Maximum likelihood estimation

 9.4 Interval Estimation of Mean and Variance for Normal Population

9.4.1 The case for a single normal population

9.4.2 The case for two populations N(y1,□),N(y2 ,□)

 Exercise 9

Chapter 10 Hypothesis Testing

10.1 General Concepts Used in Hypothesis Testing

10.1.1 Statistical hypothesis

10.1.2 Two types of errors

10.1.3 Testing a statistical hypothesis

10.2 Hypothesis Test for a Single Normal Population Parameter

10.2.1 Hypothesis test for mean y of a single normal population

10.2.2 Hypothesis test for variance

10.3 Hypothesis Test of Two Normal Population Parameters

10.3.1 Hypothesis test for a difference between two normal populations

10.3.2 Hypothesis test for two normal population variances

 10.4 The Relationship between Hypothesis Testing and Confidence Interval

 Exercise 10

Answers to Exercises

Appendix A Some Important Distributions

Appendix B Statistical Tables

 Table B-1 Poisson Distribution

 Table B-2 Standard Normal Distribution

 Table B-3 t-Distribution

 Table B-4 X2-Distribution

 Table B-5 F-Distribution

Appendix C Index