Chapter 1 Introduction to Probability 1.1 Introduction 1.2 Interpretations of Probability 1.3 Set Algebra 1.4 The Definition of Probability 1.5 Finite Sample Spaces 1.6 Geometry Probability Setting 1.7 Conditional Probability 1.8 Independent Events Chapter 2 Random Variable and Distribution 2.1 Random Variable 2.2 Discrete Distribution 2.3 Continuous Random Variable and Its Distribution 2.4 The Function of a Random Variable Chapter 3 Multi-Dimensional Random Variable and Distributions 3.1 Multi-Dimensional Random Variable and its Distribution 3.2 Marginal Distribution 3.3 Conditional Distribution 3.4 Independence of Random Variables 3.5 Functions of Two or More Random Variables Chapter 4 Expectation 4.1 Expectation of Random Variable 4.2 Variance and Moments 4.3 Covariance and Correlation 4.4 Covariance Matrix Chapter 5 Limit Theorem 5.1 Law of Large Numbers 5.2 the Central Limit Theorem Chapter 6 Samples and Sampling Distribution 6.1 Random Samples 6.2 Statistics and Numerical Characteristics of Sample 6.3 Sampling Distribution 6.4 Distributions of Sample Mean and Sample Variance with Normal Distribution Chapter 7 Estimation of Parameters 7.1 Point Estimation， Moment Estimation and Maximum Likehood Estimators 7.2 the Evaluation Criteria of Estimators 7.3 Estimation of Intervals 7.4 Interval Estimation of Normal Population Parameters 7.5 One-Sided Confidence Interval Chapter 8 Testing Hypotheses 8.1 Problem of Testing Hypotheses 8.2 the Testing of Hypotheses of the Mean of the Normal Distribution 8.3 Testing Hypotheses about Variance of Normal Distribution 8.4 Equivalence of Tests and Confidence Sets 8.5 Test of Fit of Population Distribution 8.6 Testing of Hypotheses Using p-value Chapter 9 Simple Linear Regression 9.1 the Method of Regression 9.2 Estimation and Inference in Simple Linear Regression Solutions for Exercises References
