Machine generated contents note: 1.Probability and Distributions -- 1.1.Introduction -- 1.2.Set Theory -- 1.3.The Probability Set Function -- 1.4.Conditional Probability and Independence -- 1.5.Random Variables -- 1.6.Discrete Random Variables -- 1.6.1.Transformations -- 1.7.Continuous Random Variables -- 1.7.1.Transformations -- 1.8.Expectation of a Random Variable -- 1.9.Some Special Expectations -- 1.10.Important Inequalities -- 2.Multivariate Distributions -- 2.1.Distributions of Two Random Variables -- 2.1.1.Expectation -- 2.2.Transformations: Bivariate Random Variables -- 2.3.Conditional Distributions and Expectations -- 2.4.The Correlation Coefficient -- 2.5.Independent Random Variables -- 2.6.Extension to Several Random Variables -- 2.6.1.Multivariate Variance-Covariance Matrix -- 2.7.Transformations for Several Random Variables -- 2.8.Linear Combinations of Random Variables -- 3.Some Special Distributions -- 3.1.The Binomial and Related Distributions --

Contents note continued: 3.2.The Poisson Distribution -- 3.3.The Γ, Χ2, and β Distributions -- 3.4.The Normal Distribution -- 3.4.1.Contaminated Normals -- 3.5.The Multivariate Normal Distribution -- 3.5.1.Applications -- 3.6.t- and F-Distributions -- 3.6.1.The t-distribution -- 3.6.2.The F-distribution -- 3.6.3.Student's Theorem -- 3.7.Mixture Distributions -- 4.Some Elementary Statistical Inferences -- 4.1.Sampling and Statistics -- 4.1.1.Histogram Estimates of pmfs and pdfs -- 4.2.Confidence Intervals -- 4.2.1.Confidence Intervals for Difference in Means -- 4.2.2.Confidence Interval for Difference in Proportions -- 4.3.Confidence Intervals for Parameters of Discrete Distributions -- 4.4.Order Statistics -- 4.4.1.Quantiles -- 4.4.2.Confidence Intervals for Quantiles -- 4.5.Introduction to Hypothesis Testing -- 4.6.Additional Comments About Statistical Tests -- 4.7.Chi-Square Tests -- 4.8.The Method of Monte Carlo -- 4.8.1.Accept-Reject Generation Algorithm --

Contents note continued: 4.9.Bootstrap Procedures -- 4.9.1.Percentile Bootstrap Confidence Intervals -- 4.9.2.Bootstrap Testing Procedures -- 4.10.Tolerance Limits for Distributions -- 5.Consistency and Limiting Distributions -- 5.1.Convergence in Probability -- 5.2.Convergence in Distribution -- 5.2.1.Bounded in Probability -- 5.2.2.Δ-Method -- 5.2.3.Moment Generating Function Technique -- 5.3.Central Limit Theorem -- 5.4.Extensions to Multivariate Distributions -- 6.Maximum Likelihood Methods -- 6.1.Maximum Likelihood Estimation -- 6.2.Rao-Cramer Lower Bound and Efficiency -- 6.3.Maximum Likelihood Tests -- 6.4.Multiparameter Case: Estimation -- 6.5.Multiparameter Case: Testing -- 6.6.The EM Algorithm -- 7.Sufficiency -- 7.1.Measures of Quality of Estimators -- 7.2.A Sufficient Statistic for a Parameter -- 7.3.Properties of a Sufficient Statistic -- 7.4.Completeness and Uniqueness -- 7.5.The Exponential Class of Distributions -- 7.6.Functions of a Parameter --

Contents note continued: 7.7.The Case of Several Parameters -- 7.8.Minimal Sufficiency and Ancillary Statistics -- 7.9.Sufficiency, Completeness, and Independence -- 8.Optimal Tests of Hypotheses -- 8.1.Most Powerful Tests -- 8.2.Uniformly Most Powerful Tests -- 8.3.Likelihood Ratio Tests -- 8.4.The Sequential Probability Ratio Test -- 8.5.Minimax and Classification Procedures -- 8.5.1.Minimax Procedures -- 8.5.2.Classification -- 9.Inferences About Normal Models -- 9.1.Quadratic Forms -- 9.2.One-Way ANOVA -- 9.3.Noncentral Χ2 and F-Distributions -- 9.4.Multiple Comparisons -- 9.5.The Analysis of Variance -- 9.6.A Regression Problem -- 9.7.A Test of Independence -- 9.8.The Distributions of Certain Quadratic Forms -- 9.9.The Independence of Certain Quadratic Forms -- 10.Nonparametric and Robust Statistics -- 10.1.Location Models -- 10.2.Sample Median and the Sign Test -- 10.2.1.Asymptotic Relative Efficiency -- 10.2.2.Estimating Equations Based on the Sign Test --

Contents note continued: 10.2.3.Confidence Interval for the Median -- 10.3.Signed-Rank Wilcoxon -- 10.3.1.Asymptotic Relative Efficiency -- 10.3.2.Estimating Equations Based on Signed-Rank Wilcoxon -- 10.3.3.Confidence Interval for the Median -- 10.4.Mann-Whitney-Wilcoxon Procedure -- 10.4.1.Asymptotic Relative Efficiency -- 10.4.2.Estimating Equations Based on the Mann-Whitney-Wilcoxon -- 10.4.3.Confidence Interval for the Shift Parameter Δ -- 10.5.General Rank Scores -- 10.5.1.Efficacy -- 10.5.2.Estimating Equations Based on General Scores -- 10.5.3.Optimization: Best Estimates -- 10.6.Adaptive Procedures -- 10.7.Simple Linear Model -- 10.8.Measures of Association -- 10.8.1.Kendall's τ -- 10.8.2.Spearman's Rho -- 10.9.Robust Concepts -- 10.9.1.Location Model -- 10.9.2.Linear Model -- 11.Bayesian Statistics -- 11.1.Subjective Probability -- 11.2.Bayesian Procedures -- 11.2.1.Prior and Posterior Distributions -- 11.2.2.Bayesian Point Estimation --

Contents note continued: 11.2.3.Bayesian Interval Estimation -- 11.2.4.Bayesian Testing Procedures -- 11.2.5.Bayesian Sequential Procedures -- 11.3.More Bayesian Terminology and Ideas -- 11.4.Gibbs Sampler -- 11.5.Modern Bayesian Methods -- 11.5.1.Empirical Bayes -- A.Mathematical Comments -- A.1.Regularity Conditions -- A.2.Sequences -- B.R Functions -- C.Tables of Distributions -- D.Lists of Common Distributions -- E.References -- F.Answers to Selected Exercises.