工科概率统计(英文版)/魏军强

Chapter 1 Probability and Its Properties
1．1 Basic Probability Concepts
1．2 Axioms and Properties of Probability
1．2．1 Axioms Definition of Probability
1．2．2 Properties of Probability
1．3 Classical Probability and Counting Techniques
1．3．1 Counting Principles
1．3．2 Classical Probability
1．4 Conditional Probability， Independence of Two and Several Events
1．4．1 Conditional Probability
1．4．2 Independence
1．5 Law of Total Probability and Bayes' Theorem
Exercises

Chapter 2 Random Variables and Their Distributions
2．1 Random Variables
2．2 Distribution of a Random Variable and Distribution Function
2．3 Classical Discrete Random Variables and Continuous Random Variables
2．3．1 Discrete Distribution
2．3．2 Continuous Distribution
2．4 Distribution of Functions of a Random Variable
Exercises

Chapter 3 Random Vectors and Their Distributions
3．1 Jointly Distributed Random Variables
3．2 Marginal Distribution and Conditional Distribution of Two Random Variables
3．3 Independent Random Variables
3．4 Distribution of Functions of Two Random Variables
Exercises

Chapter 4 Expectations and Moments
4．1 Mathematical Expectation and Its Properties
4．1．1 Mathematical Expectation
4．1．2 Properties of the Expectation
4．2 Variance and Its Properties
4．2．1 Definition of the Variance
4．2．2 Properties of the Variance
4．3 Expectations and Variances of Special Probability Distributions
4．3．1 Case for Common Discrete Random Variables
4．3．2 Case for Common Continuous Random Variables
4．4 Moments
4．4．1 Covariance and Correlation Coefficients
4．4．2 Moments
Exercises

Chapter 5 The Law of Large Numbers and the Central Limit Theorem
5．1 The Law of Large Numbers and Its Applications
5．1．1 Chebyshev's Inequality
5．1．2 The Law of Large Numbers
5．2 The Central Limit Theorem and Its Applications
Exercises

Chapter 6 Basic Conceptions of Statistics
6．1 Basic Conceptions of Sampling
6．2 Descriptive Statistics
6．2．1 Summarizing Data-Numerical Methods
6．2．2 Summarizing Data-Graphical Methods
6．3 Fundamental Sampling Distributions
6．3．1 The Chi-squared Distribution
6．3．2 The t-Distribution
6．3．3 The F-Distribution
6．4 Sampling Distribution Theorems
Exercises
……

Chapter 7 Parameter Estimation
Chapter 8 Hypothesis Testing
Chapter 9 Understanding Monte Carlo Method and Statistics Software

Appendix A Tables
Bibliography