Praise for the First Edition "...an excellent textbook ...well organized and neatly written." --Mathematical Reviews "...amazingly interesting ..." --Technometrics Thoroughly updated to showcase the interrelationships between probability, statistics, and stochastic processes, Probability, Statistics, and Stochastic Processes, Second Edition prepares readers to collect, analyze, and characterize data in their chosen fields. Beginning with three chapters that develop probability theory and introduce the axioms of probability, random variables, and joint distributions, the book goes on to present limit theorems and simulation. The authors combine a rigorous, calculus-based development of theory with an intuitive approach that appeals to readers' sense of reason and logic. Including more than 400 examples that help illustrate concepts and theory, the Second Edition features new material on statistical inference and a wealth of newly added topics, including: * Consistency of point estimators * Large sample theory * Bootstrap simulation * Multiple hypothesis testing * Fisher's exact test and Kolmogorov-Smirnov test * Martingales, renewal processes, and Brownian motion * One-way analysis of variance and the general linear model Extensively class-tested to ensure an accessible presentation, Probability, Statistics, and Stochastic Processes, Second Edition is an excellent book for courses on probability and statistics at the upper-undergraduate level. The book is also an ideal resource for scientists and engineers in the fields of statistics, mathematics, industrial management, and engineering.
Preface v 1. Basic Probability Theory 1 1.1 Introduction 1 1.2 Sample Spaces and Events 3 1.3 The Axioms of Probability 7 1.4 Finite Sample Spaces and Combinatorics 16 1.5 Conditional Probability and Independence 29 1.6 The Law of Total Probability and Bayes' Formula 43 2. Random Variables 79 2.1 Introduction 79 2.2 Discrete Random Variables 81 2.3 Continuous Random Variables 86 2.4 Expected Value and Variance 99 2.5 Special Discrete Distributions 115 2.6 The Exponential Distribution 128 2.7 The Normal Distribution 132 2.8 Other Distributions 137 2.9 Location Parameters 142 2.10 The Failure Rate Function 145 3. Joint Distributions 161 3.1 Introduction 161 3.2 The Joint Distribution Function 161 3.3 Discrete Random Vectors 163 3.4 Jointly Continuous Random Vectors 166 3.5 Conditional Distributions and Independence 169 3.6 Functions of Random Vectors 178 3.7 Conditional Expectation 191 3.8 Covariance and Correlation 202 3.9 The Bivariate Normal Distribution 216 3.10 Multidimensional Random Vectors 223 3.11 Generating Functions 238 3.12 The Poisson Process 248 4. Limit Theorems 271 4.1 Introduction 271 4.2 The Law of Large Numbers 272 4.3 The Central Limit Theorem 276 4.4 Convergence in Distribution 283 5. Simulation 289 5.1 Introduction 289 5.2 Random-Number Generation 290 5.3 Simulation of Discrete Distributions 291 5.4 Simulation of Continuous Distributions 293 5.5 Miscellaneous 298 6. Statistical Inference 303 6.1 Introduction 303 6.2 Point Estimators 303 6.3 Confidence Intervals 311 6.4 Estimation Methods 321 6.5 Hypothesis Testing 336 6.6 Further Topics in Hypothesis Testing 344 6.7 Goodness of Fit 349 6.8 Bayesian Statistics 361 6.9 Nonparametric Methods 373 7. Linear Models 401 7.1 Introduction 401 7.2 Sampling Distributions 402 7.3 Single Sample Inference 406 7.4 Comparing Two Samples 412 7.5 Analysis of Variance 419 7.6 Linear Regression 426 7.7 The General Linear Model 443 8. Stochastic Processes 455 8.1 Introduction 455 8.2 Discrete-Time Markov Chains 456 8.3 Random Walks and Branching Processes 476 8.4 Continuous-Time Markov Chains 488 8.5 Martingales 506 8.6 Renewal Processes 517 8.7 Brownian Motion 522 Appendix A. Tables 541 Appendix B. Answers to Selected Problems 551 References 563 Index 565
