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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