Probability, Statistics, and Stochastic Processes, Second Edition

Description

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 estimatorsLarge sample theoryBootstrap simulationMultiple hypothesis testingFisher's exact test and Kolmogorov-Smirnov testMartingales, renewal processes, and Brownian motionOne-way analysis of variance and the general linear modelExtensively 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.Table of ContentsPreface xiPreface to the First Edition xiii1 Basic Probability Theory 11.1 Introduction 11.2 Sample Spaces and Events 31.3 The Axioms of Probability 71.4 Finite Sample Spaces and Combinatorics 151.4.1 Combinatorics 171.5 Conditional Probability and Independence 271.6 The Law of Total Probability and Bayes’ Formula 41Problems 632 Random Variables 762.1 Introduction 762.2 Discrete Random Variables 772.3 Continuous Random Variables 822.4 Expected Value and Variance 952.5 Special Discrete Distributions 1112.6 The Exponential Distribution 1232.7 The Normal Distribution 127