Chapter 1 Events and Probabilities
1.1 Random phenomena and statistical regularity
1.1.1 Random phenomena
1.1.2 The statistical definition of probability
1.2 Classical probability models
1.2.1 Sample points and sample spaces
1.2.2 Classical probability models
1.2.3 Geometric probability models
1.3 The axiomatic definition of probability
1.3.1 Events
1.3.2 Probability space
1.3.3 Continuity of probability measure
1.4 Conditional probability and independent events
1.4.1 Conditional probability
1.4.2 Total probability formula and Bayes’rule
1.4.3 Independent events
Chapter 2 Random Variables and Distribution Functions
2.1 Discrete random variables
2.1.1 The concept of random variables
2.1.2 Discrete random variables
2.2 Distribution functions and continuous random variables
2.2.1 Distribution functions
2.2.2 Continuous random variables and density functions
2.2.3 Typical continuous random variables
2.3 Random vectors
2.3.1 Discrete random vectors
2.3.2 Joint distribution functions
2.3.3 Continuous random vectors
2.4 Conditional distributions and independence
2.4.1 Conditional distributions
2.4.2 I ndependence of random variables
2.5 Functions of random variables
2.5.1 Functions of discrete random variables
2.5.2 Functions of continuous random variables
2.5.3 Functions of continuous random vectors
2.5.4 Transforms of random vectors
2.5.5 Important distributions in statistics
Chapter 3 Numerical Characteristics and Characteristic Functions
3.1 Mathematical expectations
3.1.1 Expectations for discrete random variables
3.1.2 Expectations of continuous random variables
……
Chapter 4 Probability Limit Theorems
Appendix A Distribution of Typical Random Variables
Appendix B Tables
Index
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