Probability, Statistics, and Stochastic Processes, Second Edition

✍ Scribed by Peter Olofsson, Mikael Andersson

• Publisher: Wiley
• Year: 2012
• Tongue: English
• Leaves: 574
• Edition: 2nd
• Category: Library

✦ Synopsis

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.

Table of Contents

Preface xi

Preface to the First Edition xiii

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 15

1.4.1 Combinatorics 17

1.5 Conditional Probability and Independence 27

1.6 The Law of Total Probability and Bayes’ Formula 41

Problems 63

2 Random Variables 76

2.1 Introduction 76

2.2 Discrete Random Variables 77

2.3 Continuous Random Variables 82

2.4 Expected Value and Variance 95

2.5 Special Discrete Distributions 111

2.6 The Exponential Distribution 123

2.7 The Normal Distribution 127