Chapter１ 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
Exercise１
Chapter２ 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 Useful Continuous Distributions
２．７ Functions of a Random Variable
Exercise２
Chapter３ Multivariate Probability Distributions
３．１ Bivariate Distributions
３．２ Marginal Distributions
３．３ Conditional Distributions
３．４ Independent Random Variables
３．５ Functions of TwoorMoreRandom Variables
Exercise３
Chapter４ 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 CovarianceMatrix
Exercise４
Chapter５ Large Random Samples
５．１ The Law of Large Numbers
５．２ The Central Limit Theorem
Exercise５
Chapter６ 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
Exercise６
Chapter７ 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
Exercise７
Chapter８ 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
Exercise８
Appendix A Binomial Probability Distribution
Appendix B Poisson Cumulative Distribution
Appendix C Standard Normal Table
Appendix D t-distribution Upper Quantiles tn
Appendix E ２-distribution Upper Quantiles ２n
Appendix F F-distribution Upper Quantiles Fn１,n２
Appendix G Some Common Probability Distributions
Bibliography
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