本书是在教育部大力推进双语教学的大背景下推出的,结合当前开展概率论与数理统计课程双语教学的实际情况,以教育部数学与统计学教学指导委员会制定的本课程教学基本要求为依据,同时兼顾概率论与数理统计课程的考研大纲要求,突出统计学的思想,着重讲解概率论与数理统计的基本概念､基本理论及基本方法,注重体现概率统计在各个领域中的广泛应用,将大量的实际应用贯穿于理论讲解的始终,将经典和近代统计思想与算法阐述得更为具体｡
本书介绍了随机事件及其概率､随机变量与概率分布､连续型随机变量､多维随机变量和中心极限定理､统计描述､参数估计､假设检验､非参数统计､回归分析以及方差分析｡本书汲取了英文原版教材中流行的直观､灵活的教学方法及通过图表和案例进行概率统计教学的长处,突出应用概率统计技能培养的特点,强调学生分析问题和解决问题的实际能力,具有覆盖面全､实用性强､示例与习题丰富､内容新颖､图解清晰､难易适度等特点｡
本书邀请了一些有英美留学背景的人士进行编写和审定,在文字表述方面,英文语言简单易懂,写作风格简约｡本书已在校内外经过多次试用并取得了较好的教学效果,可供高等学校理工非数学类专业概率论与数理统计课程双语教学使用｡
- 前辅文
- 1 Introduction
- 2 Probability
- 2.1 Sample Space
- 2.2 Events
- 2.3 Probability of Events
- 2.4 Laws of Probability
- 2.5 Conditional Probability
- 2.6 Bayes’ Rule
- Exercises 2
- 3 Random Variables
- 3.1 Definition of Random Variables
- 3.2 Discrete Random Variables
- 3.3 Expectation and Variance
- 3.4 Binomial Distribution
- 3.5 Poisson Distribution
- Exercises 3
- 4 Continuous Random Variables
- 4.1 Continuous Random Variables
- 4.2 Uniform Distribution
- 4.3 Normal Distribution
- 4.4 Normal Approximation to the Binomial Distribution
- 4.5 Exponential Distribution
- 4.6 Function of Random Variables
- 4.7 Chebyshevs Theorem
- Exercises 4
- 5 Random Vectors and Joint Probability Distributions
- 5.1 Concept of Joint Probability Distributions
- 5.2 Conditional Distribution
- 5.3 Statistical Independent
- 5.4 Covariance and Correlation
- 5.5 Law of Large Numbers and Central Limit Theorem
- Exercises 5
- 6 Fundamental Sampling Distributions and Data Descriptions
- 6.1 Analysis of Data
- 6.2 Random Sampling
- 6.3 Statistics
- 6.4 Sample Distributions
- 6.5 Chi square Distribution
- 6.6 Student’s Distribution(t Distribution)
- 6.7 F Distribution
- Exercises 6
- 7 Estimation Problems
- 7.1 Point Estimation
- 7.2 Interval Estimation
- 7.3 Determination of the Sample Size
- 7.4 Maximum Likelihood Estimation
- Exercises 7
- 8 Testing Hypothesis
- 8.1 Statistical Hypothesis:General Concepts
- 8.2 Testing a Statistical Hypothesis
- 8.3 Hypothesis Concerning Mean
- 8.4 Hypothesis Concerning Variance
- 8.5 Relationship to Confidence Interval Estimation
- 8.6 Tests for Proportion
- 8.7 Tests for Independence
- 8.8 Goodness of Fit Test
- Exercises 8
- 9 Nonparametric Statistics
- 9.1 Sign Test
- 9.2 Rank Sum Test
- 9.3 Signed Rank Test
- Exercises 9
- 10 Regression and Correlation
- 10.1 Introduction
- 10.2 Simple Linear Regression Equation
- 10.3 Parameter Estimation
- 10.4 Tests the Usefulness of the Linear Regression Model
- 10.5 Predictions
- 10.6 Multiple Linear Regression
- 10.7 Linearizable Models
- 10.8 Normal Correlation Model
- Exercises 10
- 11 Analysis of Variance
- 11.1 Introduction
- 11.2 One Way Analysis of Variance
- 11.3 Two Way Analysis of Variance
- Exercises 11
- Answer to Exercises
- Review Exercises
- Appendix
- References
