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Probability and Stochastic Processes: A Friendly Introduction for Electrical and Computer Engineers, 3rd Edition

Book Description

This text introduces engineering students to probability theory and stochastic processes. Along with thorough mathematical development of the subject, the book presents intuitive explanations of key points in order to give students the insights they need to apply math to practical engineering problems. The first seven chapters contain the core material that is essential to any introductory course. In one-semester undergraduate courses, instructors can select material from the remaining chapters to meet their individual goals. Graduate courses can cover all chapters in one semester.

Table of Contents

  1. Coverpage
  2. Features of this Text
  3. Titlepage
  4. Copyright
  5. Dedication
  6. Preface
  7. Contents
  8. 1 Experiments, Models, and Probabilities
    1. Getting Started with Probability
    2. 1.1 Set Theory
    3. 1.2 Applying Set Theory to Probability
    4. 1.3 Probability Axioms
    5. 1.4 Conditional Probability
    6. 1.5 Partitions and the Law of Total Probability
    7. 1.6 Independence
    8. 1.7 MATLAB
      1. Problems
  9. 2 Sequential Experiments
    1. 2.1 Tree Diagrams
    2. 2.2 Counting Methods
    3. 2.3 Independent Trials
    4. 2.4 Reliability Analysis
    5. 2.5 MATLAB
      1. Problems
  10. 3 Discrete Random Variables
    1. 3.1 Definitions
    2. 3.2 Probability Mass Function
    3. 3.3 Families of Discrete Random Variables
    4. 3.4 Cumulative Distribution Function (CDF)
    5. 3.5 Averages and Expected Value
    6. 3.6 Functions of a Random Variable
    7. 3.7 Expected Value of a Derived Random Variable
    8. 3.8 Variance and Standard Deviation
    9. 3.9 MATLAB
      1. Problems
  11. 4 Continuous Random Variables
    1. 4.1 Continuous Sample Space
    2. 4.2 The Cumulative Distribution Function
    3. 4.3 Probability Density Function
    4. 4.4 Expected Values
    5. 4.5 Families of Continuous Random Variables
    6. 4.6 Gaussian Random Variables
    7. 4.7 Delta Functions, Mixed Random Variables
    8. 4.8 MATLAB
      1. Problems
  12. 5 Multiple Random Variables
    1. 5.1 Joint Cumulative Distribution Function
    2. 5.2 Joint Probability Mass Function
    3. 5.3 Marginal PMF
    4. 5.4 Joint Probability Density Function
    5. 5.5 Marginal PDF
    6. 5.6 Independent Random Variables
    7. 5.7 Expected Value of a Function of Two Random Variables
    8. 5.8 Covariance, Correlation and Independence
    9. 5.9 Bivariate Gaussian Random Variables
    10. 5.10 Multivariate Probability Models
    11. 5.11 MATLAB
      1. Problems
  13. 6 Probability Models of Derived Random Variables
    1. 6.1 PMF of a Function of Two Discrete Random Variables
    2. 6.2 Functions Yielding Continuous Random Variables
    3. 6.3 Functions Yielding Discrete or Mixed Random Variables
    4. 6.4 Continuous Functions of Two Continuous Random Variables
    5. 6.5 PDF of the Sum of Two Random Variables
    6. 6.6 MATLAB
      1. Problems
  14. 7 Conditional Probability Models
    1. 7.1 Conditioning a Random Variable by an Event
    2. 7.2 Conditional Expected Value Given an Event
    3. 7.3 Conditioning Two Random Variables by an Event
    4. 7.4 Conditioning by a Random Variable
    5. 7.5 Conditional Expected Value Given a Random Variable
    6. 7.6 Bivariate Gaussian Random Variables: Conditional PDFs
    7. 7.7 MATLAB
      1. Problems
  15. 8 Random Vectors
    1. 8.1 Vector Notation
    2. 8.2 Independent Random Variables and Random Vectors
    3. 8.3 Functions of Random Vectors
    4. 8.4 Expected Value Vector and Correlation Matrix
    5. 8.5 Gaussian Random Vectors
    6. 8.6 MATLAB
      1. Problems
  16. 9 Sums of Random Variables
    1. 9.1 Expected Values of Sums
    2. 9.2 Moment Generating Functions
    3. 9.3 MGF of the Sum of Independent Random Variables
    4. 9.4 Random Sums of Independent Random Variables
    5. 9.5 Central Limit Theorem
    6. 9.6 MATLAB
      1. Problems
  17. 10 The Sample Mean
    1. 10.1 Sample Mean: Expected Value and Variance
    2. 10.2 Deviation of a Random Variable from the Expected Value
    3. 10.3 Laws of Large Numbers
    4. 10.4 Point Estimates of Model Parameters
    5. 10.5 Confidence Intervals
    6. 10.6 MATLAB
      1. Problems
  18. 11 Hypothesis Testing
    1. 11.1 Significance Testing
    2. 11.2 Binary Hypothesis Testing
    3. 11.3 Multiple Hypothesis Test
    4. 11.4 MATLAB
      1. Problems
  19. 12 Estimation of a Random Variable
    1. 12.1 Minimum Mean Square Error Estimation
    2. 12.2 Linear Estimation of X given Y
    3. 12.3 MAP and ML Estimation
    4. 12.4 Linear Estimation of Random Variables from Random Vectors
    5. 12.5 MATLAB
      1. Problems
  20. 13 Stochastic Processes
    1. 13.1 Definitions and Examples
    2. 13.2 Random Variables from Random Processes
    3. 13.3 Independent, Identically Distributed Random Sequences
    4. 13.4 The Poisson Process
    5. 13.5 Properties of the Poisson Process
    6. 13.6 The Brownian Motion Process
    7. 13.7 Expected Value and Correlation
    8. 13.8 Stationary Processes
    9. 13.9 Wide Sense Stationary Stochastic Processes
    10. 13.10 Cross-Correlation
    11. 13.11 Gaussian Processes
    12. 13.12 MATLAB
      1. Problems
  21. Appendix A Families of Random Variables
    1. A.1 Discrete Random Variables
    2. A.2 Continuous Random Variables
  22. Appendix B A Few Math Facts
  23. References
  24. Index