Chapter 1 Introduction to Probability
1.1 Random Experiments
1.2 Sample Space
1.3 Relations and Operations between Events
1.4 The Definition of Probability
1.5 Equally Likely Outcomes Model
1.6 Conditional Probability
1.7 Total Probability and Bayes' Theorem
1.8 Independent Events
Exercise 1
Chapter 2 Random Variables and Distributions
2.1 Random Variables
2.2 Cumulative Distribution Function
2.3 Discrete Distributions
2.4 Some Common Discrete Distributions
2.5 Continuous Distributions
2.6 Some Usefu1 Continuous Distributions
2.7 Functions of a Random Variable
Exercise 2
Chapter 3 Multivariate Probability Distributions
3.1 Bivariate Distributions
3.2 Marginal Distributions
3.3 Conditional Distrmutions
3.4 Independent Random Variables
3.5 Functions of Two or More Random Variables
Exercise 3
Chapter 4 Characteristics of Random Variables
4.1 The Expectation of a Random Variable
4.2 Variance
4.3 The Characteristics of Some Common Distributions
4.4 Chebyshev's Inequality
4.5 Covariance and Correlation Coefficient
4.6 Moment and Covariance Matrix
Exereise 4
Chapter 5 Large Random Samples
5.1 The Law of Large Numbers
5.2 The CentraI Limit Theorem
Exercise 5
Chapter 6 Estimation
6.1 Population and Sample
6.2 Moment Estimation
6.3 Maximum Likelihood Estimation
6.4 Properties of Estimators
6.5 Three Important Distributions
6.6 Confidence Intervals
Exercise 6
Chapter 7 Hypothesis Testing
7.1 Basics of Hypothesis Testing
7.2 Hypothesis Tests for a Population Mean
7.3 Testing Differences between Means
7.4 Hypothesis Tests for One or Two Variances
7.5 Goodness of Fit Tests
Exercise 7
Chapter 8 Linear Regression
8.1 Linear Regression Model
8.2 Least Squares Estimation
8.3 Properties of Linear Regression Estimators
8.4 Inferences Concerning the Slope
8.5 Regression Validity
8.6 Confidence Interval for Mean Response
8.7 Inference for Prediction
Exercise 8
Chapter 9 Introduction to R language
9.1 Features of R Language
9.2 R Installation
9.3 Vector, Matrix and Data Frame
9.4 Loop and Branch Control Statements
9.5 Common Probability Distributions
9.6 Some Examples
Appendix A Binomial Probability Distribution
Appendix B Poisson Cmnulative Distribution
Appendix C Standard Normal Table
Appendix D t-distribution Upper Quantiles tα(n)
Appendix E f-distribution Upper QuantilessX2α(n)
Appendix F F-distribution Upper Quantiles R(n1，n2)
Appendix G Some Common Probability Distributions
Bibliography
