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Fundamentals of Applied Probability and Random Processes

Book Description

The long-awaited revision of Fundamentals of Applied Probability and Random Processes expands on the central components that made the first edition a classic. The title is based on the premise that engineers use probability as a modeling tool, and that probability can be applied to the solution of engineering problems. Engineers and students studying probability and random processes also need to analyze data, and thus need some knowledge of statistics. This book is designed to provide students with a thorough grounding in probability and stochastic processes, demonstrate their applicability to real-world problems, and introduce the basics of statistics. The book's clear writing style and homework problems make it ideal for the classroom or for self-study.

Table of Contents

  1. Cover image
  2. Title page
  3. Table of Contents
  4. Copyright
  5. Acknowledgment
  6. Preface to the Second Edition
  7. Preface to First Edition
  8. Chapter 1: Basic Probability Concepts
    1. Abstract
    2. 1.1 Introduction
    3. 1.2 Sample Space and Events
    4. 1.3 Definitions of Probability
    5. 1.4 Applications of Probability
    6. 1.5 Elementary Set Theory
    7. 1.6 Properties of Probability
    8. 1.7 Conditional Probability
    9. 1.8 Independent Events
    10. 1.9 Combined Experiments
    11. 1.10 Basic Combinatorial Analysis
    12. 1.11 Reliability Applications
    13. 1.12 Chapter Summary
    14. 1.13 Problems
  9. Chapter 2: Random Variables
    1. Abstract
    2. 2.1 Introduction
    3. 2.2 Definition of a Random Variable
    4. 2.3 Events Defined by Random Variables
    5. 2.4 Distribution Functions
    6. 2.5 Discrete Random Variables
    7. 2.6 Continuous Random Variables
    8. 2.7 Chapter Summary
    9. 2.8 Problems
  10. Chapter 3: Moments of Random Variables
    1. Abstract
    2. 3.1 Introduction
    3. 3.2 Expectation
    4. 3.3 Expectation of Nonnegative Random Variables
    5. 3.4 Moments of Random Variables and the Variance
    6. 3.5 Conditional Expectations
    7. 3.6 The Markov Inequality
    8. 3.7 The Chebyshev Inequality
    9. 3.8 Chapter Summary
    10. 3.9 Problems
  11. Chapter 4: Special Probability Distributions
    1. Abstract
    2. 4.1 Introduction
    3. 4.2 The Bernoulli Trial and Bernoulli Distribution
    4. 4.3 Binomial Distribution
    5. 4.4 Geometric Distribution
    6. 4.5 Pascal Distribution
    7. 4.6 Hypergeometric Distribution
    8. 4.7 Poisson Distribution
    9. 4.8 Exponential Distribution
    10. 4.9 Erlang Distribution
    11. 4.10 Uniform Distribution
    12. 4.11 Normal Distribution
    13. 4.12 The Hazard Function
    14. 4.13 Truncated Probability Distributions
    15. 4.14 Chapter Summary
    16. 4.15 Problems
  12. Chapter 5: Multiple Random Variables
    1. Abstract
    2. 5.1 Introduction
    3. 5.2 Joint CDFs of Bivariate Random Variables
    4. 5.3 Discrete Bivariate Random Variables
    5. 5.4 Continuous Bivariate Random Variables
    6. 5.5 Determining Probabilities from a Joint CDF
    7. 5.6 Conditional Distributions
    8. 5.7 Covariance and Correlation Coefficient
    9. 5.8 Multivariate Random Variables
    10. 5.9 Multinomial Distributions
    11. 5.10 Chapter Summary
    12. 5.11 Problems
  13. Chapter 6: Functions of Random Variables
    1. Abstract
    2. 6.1 Introduction
    3. 6.2 Functions of One Random Variable
    4. 6.3 Expectation of a Function of One Random Variable
    5. 6.4 Sums of Independent Random Variables
    6. 6.5 Minimum of Two Independent Random Variables
    7. 6.6 Maximum of Two Independent Random Variables
    8. 6.7 Comparison of the Interconnection Models
    9. 6.8 Two Functions of Two Random Variables
    10. 6.9 Laws of Large Numbers
    11. 6.10 The Central Limit Theorem
    12. 6.11 Order Statistics
    13. 6.12 Chapter Summary
    14. 6.13 Problems
  14. Chapter 7: Transform Methods
    1. Abstract
    2. 7.1 Introduction
    3. 7.2 The Characteristic Function
    4. 7.3 The <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="smallcaps">S</span>-Transform-Transform
    5. 7.4 The <span xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" class="smallcaps">Z</span>-Transform-Transform
    6. 7.5 Random Sum of Random Variables
    7. 7.6 Chapter Summary
    8. 7.7 Problems
  15. Chapter 8: Introduction to Descriptive Statistics
    1. Abstract
    2. 8.1 Introduction
    3. 8.2 Descriptive Statistics
    4. 8.3 Measures of Central Tendency
    5. 8.4 Measures of Dispersion
    6. 8.5 Graphical and Tabular Displays
    7. 8.6 Shape of Frequency Distributions: Skewness
    8. 8.7 Shape of Frequency Distributions: Peakedness
    9. 8.8 Chapter Summary
    10. 8.9 Problems
  16. Chapter 9: Introduction to Inferential Statistics
    1. Abstract
    2. 9.1 Introduction
    3. 9.2 Sampling Theory
    4. 9.3 Estimation Theory
    5. 9.4 Hypothesis Testing
    6. 9.5 Regression Analysis
    7. 9.6 Chapter Summary
    8. 9.7 Problems
  17. Chapter 10: Introduction to Random Processes
    1. Abstract
    2. 10.1 Introduction
    3. 10.2 Classification of Random Processes
    4. 10.3 Characterizing a Random Process
    5. 10.4 Crosscorrelation and Crosscovariance Functions
    6. 10.5 Stationary Random Processes
    7. 10.6 Ergodic Random Processes
    8. 10.7 Power Spectral Density
    9. 10.8 Discrete-Time Random Processes
    10. 10.9 Chapter Summary
    11. 10.10 Problems
  18. Chapter 11: Linear Systems with Random Inputs
    1. Abstract
    2. 11.1 Introduction
    3. 11.2 Overview of Linear Systems with Deterministic Inputs
    4. 11.3 Linear Systems with Continuous-time Random Inputs
    5. 11.4 Linear Systems with Discrete-time Random Inputs
    6. 11.5 Autoregressive Moving Average Process
    7. 11.6 Chapter Summary
    8. 11.7 Problems
  19. Chapter 12: Special Random Processes
    1. Abstract
    2. 12.1 Introduction
    3. 12.2 The Bernoulli Process
    4. 12.3 Random Walk Process
    5. 12.4 The Gaussian Process
    6. 12.5 Poisson Process
    7. 12.6 Markov Processes
    8. 12.7 Discrete-Time Markov Chains
    9. 12.8 Continuous-Time Markov Chains
    10. 12.9 Gambler’s Ruin as a Markov Chain
    11. 12.10 Chapter Summary
    12. 12.11 Problems
  20. Appendix: Table of CDF of the Standard Normal Random Variable
  21. Bibliography
  22. Index