Probability and Distributions Introduction About Sets Axiomatic Development of Probability Conditional Probability and Independent Events Discrete Random Variables Continuous Random Variables Some Useful Distributions Exercises and Complements Moments and Generating Functions Introduction Expectation and Variance Moments and Moment Generating Function Determination of a Distribution via MGF Probability Generating Function Exercises and Complements Multivariate Random Variables Introduction Probability Distributions Covariances and Correlation Coefficient Independence of Random Variables Bivariate Normal Distribution Correlation Coefficient and Independence Exponential Family Selected Probability Inequalities Exercises and Complements Sampling Distribution Introduction Moment Generating Function Approach Order Statistics Transformation Special Sampling Distributions Multivariate Normal Distribution Selected Reviews in Matrices Exercises and Complements Notions of Convergence Introduction Convergence in Probability Convergence in Distribution Convergence of Chi-Square, t, and F distributions Exercises and Complements Sufficiency, Completeness, and Ancillarity Introduction Sufficiency Minimal Sufficiency Information Ancillarity Completeness Exercises and Complements Point Estimation Introduction Maximum Likelihood Estimator Criteria to Compare Estimators Improved Unbiased Estimators via Sufficiency Uniformly Minimum Variance Unbiased Estimator Consistent Estimator Exercises and Complements Tests of Hypotheses Introduction Error Probabilities and Power Function Simple Null vs. Simple Alternative One-Sided Composite Alternative Simple Null vs. Two-Sided Alternative Exercises and Complements Confidence Intervals Introduction One-Sample Problems Two-Sample Problems Exercises and Complements Bayesian Methods Introduction Prior and Posterior Distributions Conjugate Prior Point Estimation Examples with a Nonconjugate Prior Exercises and Complements Likelihood Ratio and Other Tests Introduction One-Sample LR Tests: Normal Two-Sample LR Tests: Independent Normal Bivariate Normal Exercises and Complements Large-Sample Methods Introduction Maximum Likelihood Estimation Asymptotic Relative Efficiency Confidence Intervals and Tests of Hypotheses Variance Stabilizing Transformation Exercises and Complements Abbreviations, Historical Notes, and Tables Abbreviations and Notations Historical Notes Selected Statistical Tables References Answers: Selected Exercises Author Index Subject Index Complements Sampling Distribution Introduction Moment Generating Function Approach Order Statistics Transformation Special Sampling Distributions Multivariate Normal Distribution Selected Reviews in Matrices Exercises and Complements Notions of Convergence Introduction Convergence in Probability Convergence in Distribution Convergence of Chi-Square, t, and F distributions Exercises and Complements Sufficiency, Completeness, and Ancillarity Introduction Sufficiency Minimal Sufficiency Information Ancillarity Completeness Exercises and Complements Point Estimation Introduction Maximum Likelihood Estimator Criteria to Compare Estimators Improved Unbiased Estimators via Sufficiency Uniformly Minimum Variance Unbiased Estimator Consistent Estimator Exercises and Complements Tests of Hypotheses Introduction Error Probabilities and Power Function Simple Null vs. Simple Alternative One-Sided Composite Alternative Simple Null vs. Two-Sided Alternative Exercises and Complements Confidence Intervals Introduction One-Sample Problems Two-Sample Problems Exercises and Complements Bayesian Methods Introduction Prior and Posterior Distributions Conjugate Prior Point Estimation Examples with a Nonconjugate Prior Exercises and Complements Likelihood Ratio and Other Tests Introduction One-Sample LR Tests: Normal Two-Sample LR Tests: Independent Normal Bivariate Normal Exercises and Complements Large-Sample Methods Introduction Maximum Likelihood Estimation Asymptotic Relative Efficiency Confidence Intervals and Tests of Hypotheses Variance Stabilizing Transformation Exercises and Complements Abbreviations, Historical Notes, and Tables Abbreviations and Notations Historical Notes Selected Statistical Tables References Answers: Selected Exercises Author Index Subject Indexvia Sufficiency Uniformly Minimum Variance Unbiased Estimator Consistent Estimator Exercises and Complements Tests of Hypotheses Introduction Error Probabilities and Power Function Simple Null vs. Simple Alternative One-Sided Composite Alternative Simple Null vs. Two-Sided Alternative Exercises and Complements Confidence Intervals Introduction One-Sample Problems Two-Sample Problems Exercises and Complements Bayesian Methods Introduction Prior and Posterior Distributions Conjugate Prior Point Estimation Examples with a Nonconjugate Prior Exercises and Complements Likelihood Ratio and Other Tests Introduction One-Sample LR Tests: Normal Two-Sample LR Tests: Independent Normal Bivariate Normal Exercises and Complements Large-Sample Methods Introduction Maximum Likelihood Estimation Asymptotic Relative Efficiency Confidence Intervals and Tests of Hypotheses Variance Stabilizing Transformation Exercises and Complements Abbreviations, Historical Notes, and Tables Abbreviations and Notations Historical Notes Selected Statistical Tables References Answers: Selected Exercises Author Index Subject Index>Bivariate Normal Exercises and Complements Large-Sample Methods Introduction Maximum Likelihood Estimation Asymptotic Relative Efficiency Confidence Intervals and Tests of Hypotheses Variance Stabilizing Transformation Exercises and Complements Abbreviations, Historical Notes, and Tables Abbreviations and Notations Historical Notes Selected Statistical Tables References Answers: Selected Exercises Author Index Subject Index.