Probability & Statistics

1 The Axioms of Probability1. 1 Experiments1. 2 Sample Spaces and Events1. 3 Frequency and Probability1. 4 Equally Likely Outcomes1. 5 Conditional Probability1. 6 IndependenceExercise 12 Random Variables and Their Distributions2.1 Random Variables2.2 Discrete Random Variables2.3 Cumulative Distribution Functions2.4 Continuous Random Variables2.5 Functions of Random VariablesExercise 23 Multivariate Random Variables3.1 Two¡ª¡ªDimensional Random Variables3.2 Marginal Distributions3.3 Conditional Distributions3.4 Independence3.5 Distribution of Special FunctionsExercise 34 The Mean and Variance4.1 Expectations of random variables4.2 Variances of random variables4.3 Covariance & Correlation4.4 Miment and Covariance MatrixExercise5 The Law of Large Numbers and the Central Limit Theorem5.1 Chebyshev's Inequality5.2 Law of Large numbers5.3 The Central Limit TheoremExercise 56 Random Sampling6.1 Random Sampling6.1.1 Populations and Samples6.1.2 Random Sample6.2 Some Important Statistics6.2.1 The Sample Mean and the Sample Variance6.2.2 The Sample Moments6.3 Sampling Distributions6.3.1 The Chi-Square distribution6.3.2 t-Distribution6.3.3 F-Distribution6.3.4 Quantile of Order tt6.3.5 Sampling Distributions of the Sample Mean and the Sample VarianceExercise 67 Estimation Problems7.1 Introduction7.2 Point Estimation7.2.1 The Method of Moments7.2.2 The Method of Maximum Likelihood7.3 The Particular Properties of Estimators7.3.1 Unbiased Estimators7.3.2 Efficiency7.3.3 Consistency7.4 Interval Estimation7.4.1 The Estimation of Mean7.4.2 The Estimation of VarianceExercise 78 Hypothesis Testing8.1 Introduction8.2 Tests Concerning Means8.2.1 One Normal Population8.2.2 To Normal Populations8.3 Tests Concerning Variances8.3.1 One Normal Population8.3.2 Two Normal Populations8.4 The Relationship Between Hypothesis Testing and Confidence Intervals8.5 One Sample: Thex2 Goodness of Fit TestExercise 8Appendix A Some Important DistributionsAppendix B Statistical TablesAppendix C Answer To ExerciseAppendix D ÖÐÓ¢ÎĶÔÕÕ±íBibliography