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Chapter 1 Random Events and Probabilities 1.1 Random events and sample space 1.2 Relationship and operation of random events 1.3 Probability of random events 1.4 The axioms and properties of probability 1.5 Conditional Probability and Multiplication Formula 1.6 total probability formula and inverse probability formula 1.7 Independence of random events Chapter 2 Random Variables and Their Distribution 2.1 Discrete random variables and their distribution law 2.2 Distribution function of random variables 2.3 Continuous random variables and their probability density 2.4 several common continuous random variables 2.5 Distribution of random variable functions Chapter 3 Random Vectors and Their Distribution 3.1 two-dimensional random vector 3.2 two-dimensional discrete random vector 3.3 two-dimensional continuous random vector 3.4 Independence of random variables 3.5 Distribution of two random vector functions Chapter 4 Digital Features of Random Variables 4.1 Mathematical Expectations of Random Variables 4.2 Variance of random variables 4.3 Covariance and correlation coefficient 4.4 Moment and Covariance Matrix of Random Variables Chapter 5 Law of Large Numbers and Central Limit Theorem 5.1 Law of Large Numbers 5.2 Central Limit Theorem Chapter 6 Sampling Distribution 6.1 Basic concepts of mathematical statistics 6.2 sampling distribution Chapter 7 Parameter Estimation 7.1 point estimate 7.2 Evaluation criteria for estimators 7.3 Interval Estimation of a Single Normal Population 7.4 Interval Estimation of Two Normal Populations Chapter 8 Hypothesis Testing 8.1 The basic idea of hypothesis testing 8.2 Hypothesis testing of single normal population mean 8.3 Hypothesis testing of two normal population means 8.4 Hypothesis testing of single normal population variance 8.5 Hypothesis testing of two normal population variances Appendix References