Table of Contents

  • Preface
    • New to This Edition
    • Course
    • Examples and Exercises
    • Organization
    • Acknowledgments
  • Introduction to Probability Theory
    • Abstract
    • 1.1 Introduction
    • 1.2 Sample Space and Events
    • 1.3 Probabilities Defined on Events
    • 1.4 Conditional Probabilities
    • 1.5 Independent Events
    • 1.6 Bayes’ Formula
    • Exercises
    • References
  • Random Variables
    • Abstract
    • 2.1 Random Variables
    • 2.2 Discrete Random Variables
    • 2.3 Continuous Random Variables
    • 2.4 Expectation of a Random Variable
    • 2.5 Jointly Distributed Random Variables
    • 2.6 Moment Generating Functions
    • 2.7 The Distribution of the Number of Events that Occur
    • 2.8 Limit Theorems
    • 2.9 Stochastic Processes
    • Exercises
    • References
  • Conditional Probability and Conditional Expectation
    • Abstract
    • 3.1 Introduction
    • 3.2 The Discrete Case
    • 3.3 The Continuous Case
    • 3.4 Computing Expectations by Conditioning
    • 3.5 Computing Probabilities by Conditioning
    • 3.6 Some Applications
    • 3.7 An Identity for Compound Random Variables
    • Exercises
  • Markov Chains
    • Abstract
    • 4.1 Introduction
    • 4.2 Chapman–Kolmogorov Equations
    • 4.3 Classification of States
    • 4.4 Long-Run Proportions and Limiting Probabilities
    • 4.5 Some Applications
    • 4.6 Mean Time Spent in Transient States
    • 4.7 Branching Processes
    • 4.8 Time Reversible Markov Chains
    • 4.9 Markov Chain Monte Carlo Methods
    • 4.10 Markov Decision Processes
    • 4.11 Hidden Markov Chains
    • Exercises
    • References
  • The Exponential Distribution and the Poisson Process
    • Abstract
    • 5.1 Introduction
    • 5.2 The

Details

No. of pages:
784
Language:
English
Copyright:
© 2014
Published:
Imprint:
Academic Press
Electronic ISBN:
9780124081215
Print ISBN:
9780124079489