Probability, statistics, and stochastic processes

This book provides a unique andbalanced approach to probability, statistics, and stochastic processes. Readers gain a solid foundation in all three fieldsthat serves as a stepping stone to more advanced investigations into each area. The Second Edition features new coverage of analysis of variance (ANOVA), consistency and efficiency of estimators, asymptotic theory for maximum likelihood estimators, empirical distribution function and the Kolmogorov-Smirnov test, general linear models, multiple comparisons, Markov chain Monte Carlo (MCMC), Brownian motion, martingales, and renewal theory. Many new introductory problems and exercises have also been added. This book combines a rigorous, calculus-based development of theory with a more intuitive approach that appeals toreaders' sense of reason and logic, an approach developed through the author's many years of classroom experience. The book begins with three chapters thatdevelop probability theory and introduce the axioms of probability, random variables, and joint distributions. The next two chapters introduce limit theorems and simulation. Also included is a chapter on statistical inference with afocus onBayesian statistics, which is an important, though often neglected, topic for undergraduate-level texts. Markov chains in discrete and continuous time are also discussed within the book. More than 400 examples are interspersed throughout to help illustrate concepts and theory and to assist readers in developing an intuitive sense of the subject. Readers will find many of the examples to be both entertaining and thought provoking. This is also true for the carefully selected problems that appear at the end of each chapter. INDICE: Preface v1. Basic Probability Theory 11.1 Introduction 11.2 SampleSpaces and Events 31.3 The Axioms of Probability 71.4 Finite Sample Spaces and Combinatorics 161.5 Conditional Probability and Independence 291.6 The Law of Total Probability and Bayes’ Formula 432. Random Variables 792.1 Introduction 792.2 Discrete Random Variables 812.3 Continuous Random Variables 862.4 Expected Value and Variance 992.5 Special Discrete Distributions 1152.6 The Exponential Distribution 1282.7 The Normal Distribution 1322.8 Other Distributions1372.9 Location Parameters 1422.10 The Failure Rate Function 1453. Joint Distributions 1613.1 Introduction 1613.2 The Joint Distribution Function 1613.3 Discrete Random Vectors 1633.4 Jointly Continuous Random Vectors 1663.5 Conditional Distributions and Independence 1693.6 Functions of Random Vectors 1783.7 Conditional Expectation 1913.8 Covariance and Correlation 2023.9 The Bivariate Normal Distribution 2163.10 Multidimensional Random Vectors 2233.11 GeneratingFunctions 2383.12 The Poisson Process 2484. Limit Theorems 2714.1 Introduction 2714.2 The Law of Large Numbers 2724.3 The Central Limit Theorem 2764.4 Convergence in Distribution 2835. Simulation 2895.1 Introduction 2895.2 Random-Number Generation 2905.3 Simulation of Discrete Distributions 2915.4 Simulation of Continuous Distributions 2935.5 Miscellaneous 2986. Statistical Inference 3036.1 Introduction 3036.2 Point Estimators 3036.3 Confidence Intervals 3116.4 Estimation Methods 3216.5 Hypothesis Testing 3366.6 Further Topics in Hypothesis Testing 3446.7 Goodness of Fit 3496.8 Bayesian Statistics 3616.9 Nonparametric Methods 3737. Linear Models 4017.1 Introduction 4017.2 Sampling Distributions 4027.3 Single Sample Inference 4067.4 Comparing Two Samples 4127.5 Analysisof Variance 4197.6 Linear Regression 4267.7 The General Linear Model 4438. Stochastic Processes 4558.1 Introduction 4558.2 Discrete-Time Markov Chains 4568.3 Random Walks and Branching Processes 4768.4 Continuous-Time Markov Chains 4888.5 Martingales 5068.6 Renewal Processes 5178.7 Brownian Motion 522Appendix A. Tables 541Appendix B. Answers to Selected Problems 551References 563Index 565Â

• ISBN: 978-0-470-88974-9
• Editorial: John Wiley & Sons
• Encuadernacion: Cartoné
• Páginas: 576
• Fecha Publicación: 25/05/2012
• Nº Volúmenes: 1
• Idioma: Inglés