概率论与数理统计(英文版)

   本书根据编者多年的双语教学经验编写，介绍了概率论与数理统计的基本概念、原理、计算方法，以及实际应用.在编写过程中，吸取了靠前外很好教材的优点，注重理论与实践相结合，系统性强，图例丰富，突出统计思想，着力培养学生分析问题和解决实际问题的能力.本书主要内容包括概率与随机事件、随机变量及其分布、多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、参数估计、假设检验、线性回归分析.每章中精选了的实用性强的例题和习题.本书可作为高等院校理工科各专业本科生的概率论与数理统计课程双语教材，也可供工程技术人员、科技工作者参考。

   桂文豪，男，教授，2009年毕业于美国佛罗里达州立大学获统计系博士学位。毕业后曾任美国康奈尔大学博士后，美国南卫理公会大学和明尼苏达大学助理教授。自2014年开始任职于北京交通大学。中国现场统计研究会可靠性工程分会理事。长期从事概率论与数理统计的教学和科研工作。

  

Chapter1 Introduction to Probability

1.1 Random Experiments

1.2 Sample Space

1.3 Relations and Operations between Events

1.4 The Definition of Probability

1.5 Equally Likely Outcomes Model

1.6 Conditional Probability

1.7 Total Probability and Bayes' Theorem

1.8 Independent Events

Exercise1

Chapter2 Random Variables and Distributions

2.1 Random Variables

2.2 Cumulative Distribution Function

2.3 Discrete Distributions

2.4 Some Common Discrete Distributions

2.5 Continuous Distributions

2.6 Some Useful Continuous Distributions

2.7 Functions of a Random Variable

Exercise2

Chapter3 Multivariate Probability Distributions

3.1 Bivariate Distributions

3.2 Marginal Distributions

3.3 Conditional Distributions

3.4 Independent Random Variables

3.5 Functions of TwoorMoreRandom Variables

Exercise3

Chapter4 Characteristics of Random Variables

4.1 The Expectation of a Random Variable

4.2 Variance

4.3 The Characteristics of some Common Distributions

4.4 Chebyshev's Inequality

4.5 Covariance and Correlation Coefficient

4.6 Moment and CovarianceMatrix

Exercise4

Chapter5 Large Random Samples

5.1 The Law of Large Numbers

5.2 The Central Limit Theorem

Exercise5

Chapter6 Estimation

6.1 Population and Sample

6.2 Moment Estimation

6.3 Maximum Likelihood Estimation

6.4 Properties of Estimators

6.5 Three Important Distributions

6.6 Confidence Intervals

Exercise6

Chapter7 Hypothesis Testing

7.1 Basics of Hypothesis Testing

7.2 Hypothesis Tests for a Population Mean

7.3 Testing Differences between Means

7.4 Hypothesis Tests for One or Two Variances

7.5 Goodness of Fit Tests

Exercise7

Chapter8 Linear Regression

8.1 Linear Regression Model

8.2 Least Squares Estimation

8.3 Properties of Linear Regression Estimators

8.4 Inferences Concerning the Slope

8.5 Regression Validity

8.6 Confidence Interval for Mean Response

8.7 Inference for Prediction

Exercise8

Appendix A Binomial Probability Distribution

Appendix B Poisson Cumulative Distribution

Appendix C Standard Normal Table

Appendix D t-distribution Upper Quantiles tα(n)

Appendix E χ2-distribution Upper Quantiles χ2α(n)

Appendix F F-distribution Upper Quantiles Fα(n1,n2)

Appendix G Some Common Probability Distributions

Bibliography