1 The Axioms of Probability 1.1 Experiments 1.2 Sample Spaces and Events 1.3 Frequency and Probability 1.4 Equally Likely Outcomes 1.5 Conditional Probability 1.6 Independence Exercise 1 2 Random Variables and Their Distributions 2.1 Random Variables 2.2 Discrete Random Variables 2.3 Cumulative Distribution Functions 2.4 Continuous Random Variables 2.5 Functions of Random Variables Exercise 2 3 Multivariate Random Variables 3.1 Two--Dimensional Random Variables 3.2 Marginal Distributions 3.3 Conditional Distributions 3.4 Independence 3.5 Distribution of Special Functions Exercise 3 4 The Mean and Variance 4.1 Expectations of random variables 4.2 Variances of random variables 4.3 Covariance & Correlation 4.4 Miment and Covariance Matrix Exercise 5 The Law of Large Numbers and the Central Limit Theorem 5.1 Chebyshev's Inequality 5.2 Law of Large numbers 5.3 The Central Limit Theorem Exercise 5 6 Random Sampling 6.1 Random Sampling 6.1.1 Populations and Samples 6.1.2 Random Sample 6.2 Some Important Statistics 6.2.1 The Sample Mean and the Sample Variance 6.2.2 The Sample Moments 6.3 Sampling Distributions 6.3.1 The Chi-Square distribution 6.3.2 t-Distribution 6.3.3 F-Distribution 6.3.4 Quantile of Order tt 6.3.5 Sampling Distributions of the Sample Mean and the Sample Variance Exercise 6 7 Estimation Problems 7.1 Introduction 7.2 Point Estimation 7.2.1 The Method of Moments 7.2.2 The Method of Maximum Likelihood 7.3 The Particular Properties of Estimators 7.3.1 Unbiased Estimators 7.3.2 Efficiency 7.3.3 Consistency 7.4 Interval Estimation 7.4.1 The Estimation of Mean 7.4.2 The Estimation of Variance Exercise 7 8 Hypothesis Testing 8.1 Introduction 8.2 Tests Concerning Means 8.2.1 One Normal Population 8.2.2 To Normal Populations 8.3 Tests Concerning Variances 8.3.1 One Normal Population 8.3.2 Two Normal Populations 8.4 The Relationship Between Hypothesis Testing and Confidence Intervals 8.5 One Sample: Thex2 Goodness of Fit Test Exercise 8 Appendix A Some Important Distributions Appendix B Statistical Tables Appendix C Answer To Exercise Appendix D 中英文對(duì)照表 Bibliography
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