《概率论与数理统计 英文》PDF下载

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  • 作  者:孔令臣,王立春编著
  • 出 版 社:北京:北京交通大学出版社
  • 出版年份:2015
  • ISBN:9787512120242
  • 页数:156 页
图书介绍:概率论与数理统计学是一门用来搜集,分析,演绎以及呈现数据的科学,是一门与实际紧密结合的学科,现代统计学与各个领域的结合,是当代新兴科学的一大特征。因此,本课程一直是理工及管理学科专业重要的专业基础课程,在本课程的教学过程中,不仅仅是为了向学生传授相关的统计知识,使学生初步了解整个学科的知识结构、典型方法、核心概念以及统计学当前的发展现状和未来的发展趋势;更重要的是在具体的教学环节中培养学生对数据的敏感性以及运用所学专业知识发现并分析解决实际问题的能力,激发学生的积极性和创造性,掌握科学的学习方法。

Chapter 1 Probability 1

1.1 Introduction 1

1.2 Sample Space and Events 1

1.3 Axioms of Probability 5

1.4 Some Simple Propositions 6

1.5 Sample Spaces Having Equally Likely Outcomes 9

1.6 Conditional Probabilities 10

1.7 Bayes's Formula 13

1.8 Independent Events 17

Exercise 1 20

Chapter 2 Discrete Random Variables and Probability Distributions 22

2.1 Random Variables 22

2.2 Probability Distributions for Discrete Random Variables 24

2.3 The Binomial and Poisson Probability Distributions 29

Exercise 2 34

Chapter 3 Continuous Random Variables and Probability Distributions 37

3.1 Probability Density Functions 37

3.2 Cumulative Distribution Functions 38

3.3 The Normal Distributions 41

3.4 The Exponential and Gamma Distributions 44

3.5 Other Continuous Distributions 48

Exercise 3 48

Chapter 4 Joint Probability Distributions 51

4.1 Joint Distribution Functions 51

4.2 Marginal Distribution Functions 54

4.3 Conditional Distributions 57

4.4 Independent Random Variables 60

4.5 Sums of Independent Random Variables 63

4.6 Joint Probability Distribution of Function of Random Variables 66

Exercise 4 67

Chapter 5 Mathematical Expectation 70

5.1 Expectation of a Random Variable 70

5.2 Variance and Variance of sums 75

5.3 Covariance and Correlations 78

5.4 Conditional Expectation 81

5.5 Chebyshev's Theorem 84

Exercise 5 86

Chapter 6 Limit Theorems 89

6.1 The Weak Law of Large Numbers 89

6.2 The Central Limit Theorem 91

Exercise 6 94

Chapter 7 Descriptive Statistics 96

7.1 Populations and Samples 96

7.2 Measures of Center and Variability 98

7.3 Sampling Distributions 100

7.4 Chi-squared Distribution,t-Distribution and F-Distribution 107

Exercise 7 115

Chapter 8 Estimation 118

8.1 Point Estimation 119

8.2 The Particular Properties of Estimators 123

8.3 Interval Estimation 130

Exercise 8 138

Appendix 140

Reference 156