Probability theory and mathematical statistics

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Table of Contents
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
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Probability theory and mathematical statistics