Probability and Statistical Inference: (Wiley Series in Probability and Statistics)

Updated classic statistics text, with new problems and examples Probability and Statistical Inference, Third Edition helps students grasp essential concepts of statistics and its probabilistic foundations. This book focuses on the development of intuition and understanding in the subject through a wealth of examples illustrating concepts, theorems, and methods. The reader will recognize and fully understand the why and not just the how behind the introduced material. In this Third Edition, the reader will find a new chapter on Bayesian statistics, 70 new problems and an appendix with the supporting R code. This book is suitable for upper-level undergraduates or first-year graduate students studying statistics or related disciplines, such as mathematics or engineering. This Third Edition: Introduces an all-new chapter on Bayesian statistics and offers thorough explanations of advanced statistics and probability topics Includes 650 problems and over 400 examples - an excellent resource for the mathematical statistics class sequence in the increasingly popular "flipped classroom" format Offers students in statistics, mathematics, engineering and related fields a user-friendly resource Provides practicing professionals valuable insight into statistical tools Probability and Statistical Inference offers a unique approach to problems that allows the reader to fully integrate the knowledge gained from the text, thus, enhancing a more complete and honest understanding of the topic.

Table of Contents:
Preface to Third Edition xi Preface to Second Edition xiii About the Companion Website xvi 1 Experiments, Sample Spaces, and Events 1 1.1 Introduction 1 1.2 Sample Space 2 1.3 Algebra of Events 8 1.4 Infinite Operations on Events 13 2 Probability 21 2.1 Introduction 21 2.2 Probability as a Frequency 21 2.3 Axioms of Probability 22 2.4 Consequences of the Axioms 26 2.5 Classical Probability 30 2.6 Necessity of the Axioms 31 2.7 Subjective Probability 35 3 Counting 39 3.1 Introduction 39 3.2 Product Sets, Orderings, and Permutations 39 3.3 Binomial Coefficients 44 3.4 Multinomial Coefficients 56 4 Conditional Probability, Independence, and Markov Chains 59 4.1 Introduction 59 4.2 Conditional Probability 60 4.3 Partitions; Total Probability Formula 65 4.4 Bayes’ Formula 69 4.5 Independence 74 4.6 Exchangeability; Conditional Independence 80 4.7 Markov Chains* 82 5 Random Variables: Univariate Case 93 5.1 Introduction 93 5.2 Distributions of Random Variables 94 5.3 Discrete and Continuous Random Variables 102 5.4 Functions of Random Variables 112 5.5 Survival and Hazard Functions 118 6 Random Variables: Multivariate Case 123 6.1 Bivariate Distributions 123 6.2 Marginal Distributions; Independence 129 6.3 Conditional Distributions 140 6.4 Bivariate Transformations 147 6.5 Multidimensional Distributions 155 7 Expectation 163 7.1 Introduction 163 7.2 Expected Value 164 7.3 Expectation as an Integral 171 7.4 Properties of Expectation 177 7.5 Moments 184 7.6 Variance 191 7.7 Conditional Expectation 202 7.8 Inequalities 206 8 Selected Families of Distributions 211 8.1 Bernoulli Trials and Related Distributions 211 8.2 Hypergeometric Distribution 223 8.3 Poisson Distribution and Poisson Process 228 8.4 Exponential, Gamma, and Related Distributions 240 8.5 Normal Distribution 246 8.6 Beta Distribution 255 9 Random Samples 259 9.1 Statistics and Sampling Distributions 259 9.2 Distributions Related to Normal 261 9.3 Order Statistics 266 9.4 Generating Random Samples 272 9.5 Convergence 276 9.6 Central Limit Theorem 287 10 Introduction to Statistical Inference 295 10.1 Overview 295 10.2 Basic Models 298 10.3 Sampling 299 10.4 Measurement Scales 305 11 Estimation 309 11.1 Introduction 309 11.2 Consistency 313 11.3 Loss, Risk, and Admissibility 316 11.4 Efficiency 321 11.5 Methods of Obtaining Estimators 328 11.6 Sufficiency 345 11.7 Interval Estimation 359 12 Testing Statistical Hypotheses 373 12.1 Introduction 373 12.2 Intuitive Background 377 12.3 Most Powerful Tests 384 12.4 Uniformly Most Powerful Tests 396 12.5 Unbiased Tests 402 12.6 Generalized Likelihood Ratio Tests 405 12.7 Conditional Tests 412 12.8 Tests and Confidence Intervals 415 12.9 Review of Tests for Normal Distributions 416 12.10 Monte Carlo, Bootstrap, and Permutation Tests 424 13 Linear Models 429 13.1 Introduction 429 13.2 Regression of the First and Second Kind 431 13.3 Distributional Assumptions 436 13.4 Linear Regression in the Normal Case 438 13.5 Testing Linearity 444 13.6 Prediction 447 13.7 Inverse Regression 449 13.8 BLUE 451 13.9 Regression Toward the Mean 453 13.10 Analysis of Variance 455 13.11 One-Way Layout 455 13.12 Two-Way Layout 458 13.13 ANOVA Models with Interaction 461 13.14 Further Extensions 465 14 Rank Methods 467 14.1 Introduction 467 14.2 Glivenko–Cantelli Theorem 468 14.3 Kolmogorov–Smirnov Tests 471 14.4 One-Sample Rank Tests 478 14.5 Two-Sample Rank Tests 484 14.6 Kruskal–Wallis Test 488 15 Analysis of Categorical Data 491 15.1 Introduction 491 15.2 Chi-Square Tests 492 15.3 Homogeneity and Independence 499 15.4 Consistency and Power 504 15.5 2 × 2 Contingency Tables 509 15.6 r × c Contingency Tables 516 16 Basics of Bayesian Statistics 521 16.1 Introduction 521 16.2 Prior and Posterior Distributions 522 16.3 Bayesian Inference 529 16.4 Final Comments 543 Appendix A Supporting R Code 545 Appendix B Statistical Tables 551 Bibliography 555 Answers to Odd-Numbered Problems 559 Index 571

About the Author :
MAGDALENA NIEWIADOMSKA-BUGAJ, PHD, is Professor and Chair of the Statistics Department at Western Michigan University. Dr. Niewiadomska-Bugaj's areas of interest include general statistical methodology, nonparametric statistics, classification, and categorical data analysis. She has published over 50 papers, books, and book chapters in theoretical and applied statistics The late ROBERT BARTOSZY�SKI, PHD, was Professor in the Department of Statistics at The Ohio State University. His scientific contributions included research in the theory of stochastic processes and modeling biological phenomena. Throughout his career, Dr Bartoszyñski published books, book chapters, and over 100 journal articles.