Introduction to Probability

Introduction to Probability

by Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
Released December 2021
Publisher(s): Wiley
ISBN: 9781118123331

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Book description

INTRODUCTION TO PROBABILITY

Discover practical models and real-world applications of multivariate models useful in engineering, business, and related disciplines

In Introduction to Probability: Multivariate Models and Applications, a team of distinguished researchers delivers a comprehensive exploration of the concepts, methods, and results in multivariate distributions and models. Intended for use in a second course in probability, the material is largely self-contained, with some knowledge of basic probability theory and univariate distributions as the only prerequisite.

This textbook is intended as the sequel to Introduction to Probability: Models and Applications. Each chapter begins with a brief historical account of some of the pioneers in probability who made significant contributions to the field. It goes on to describe and explain a critical concept or method in multivariate models and closes with two collections of exercises designed to test basic and advanced understanding of the theory.

A wide range of topics are covered, including joint distributions for two or more random variables, independence of two or more variables, transformations of variables, covariance and correlation, a presentation of the most important multivariate distributions, generating functions and limit theorems. This important text:

  • Includes classroom-tested problems and solutions to probability exercises
  • Highlights real-world exercises designed to make clear the concepts presented
  • Uses Mathematica software to illustrate the text’s computer exercises
  • Features applications representing worldwide situations and processes
  • Offers two types of self-assessment exercises at the end of each chapter, so that students may review the material in that chapter and monitor their progress

Perfect for students majoring in statistics, engineering, business, psychology, operations research and mathematics taking a second course in probability, Introduction to Probability: Multivariate Models and Applications is also an indispensable resource for anyone who is required to use multivariate distributions to model the uncertainty associated with random phenomena.

Table of contents

  1. COVER
  2. TITLE PAGE
  3. COPYRIGHT
  4. DEDICATION
  5. PREFACE
  6. ACKNOWLEDGMENTS
  7. CHAPTER 1: TWO‐DIMENSIONAL DISCRETE RANDOM VARIABLES AND DISTRIBUTIONS
    1. 1.1 INTRODUCTION
    2. 1.2 JOINT PROBABILITY FUNCTION
    3. 1.3 MARGINAL DISTRIBUTIONS
    4. 1.4 EXPECTATION OF A FUNCTION
    5. 1.5 CONDITIONAL DISTRIBUTIONS AND EXPECTATIONS
    6. 1.6 BASIC CONCEPTS AND FORMULAS
    7. 1.7 COMPUTATIONAL EXERCISES
    8. 1.8 SELF‐ASSESSMENT EXERCISES
    9. 1.9 REVIEW PROBLEMS
    10. 1.10 APPLICATIONS
    11. KEY TERMS
  8. CHAPTER 2: TWO‐DIMENSIONAL CONTINUOUS RANDOM VARIABLES AND DISTRIBUTIONS
    1. 2.1 INTRODUCTION
    2. 2.2 JOINT DENSITY FUNCTION
    3. 2.3 MARGINAL DISTRIBUTIONS
    4. 2.4 EXPECTATION OF A FUNCTION
    5. 2.5 CONDITIONAL DISTRIBUTIONS AND EXPECTATIONS
    6. 2.6 GEOMETRIC PROBABILITY
    7. 2.7 BASIC CONCEPTS AND FORMULAS
    8. 2.8 COMPUTATIONAL EXERCISES
    9. 2.9 SELF‐ASSESSMENT EXERCISES
    10. 2.10 REVIEW PROBLEMS
    11. 2.11 APPLICATIONS
    12. KEY TERMS
  9. CHAPTER 3: INDEPENDENCE AND MULTIVARIATE DISTRIBUTIONS
    1. 3.1 INTRODUCTION
    2. 3.2 INDEPENDENCE
    3. 3.3 PROPERTIES OF INDEPENDENT RANDOM VARIABLES
    4. 3.4 MULTIVARIATE JOINT DISTRIBUTIONS
    5. 3.5 INDEPENDENCE OF MORE THAN TWO VARIABLES
    6. 3.6 DISTRIBUTION OF AN ORDERED SAMPLE
    7. 3.7 BASIC CONCEPTS AND FORMULAS
    8. 3.8 COMPUTATIONAL EXERCISES
    9. 3.9 SELF‐ASSESSMENT EXERCISES
    10. 3.10 REVIEW PROBLEMS
    11. 3.11 APPLICATIONS
    12. KEY TERMS
  10. CHAPTER 4: TRANSFORMATIONS OF VARIABLES
    1. 4.1 INTRODUCTION
    2. 4.2 JOINT DISTRIBUTION FOR FUNCTIONS OF VARIABLES
    3. 4.3 DISTRIBUTIONS OF SUM, DIFFERENCE, PRODUCT AND QUOTIENT
    4. 4.4 χ2, t AND F DISTRIBUTIONS
    5. 4.5 BASIC CONCEPTS AND FORMULAS
    6. 4.6 COMPUTATIONAL EXERCISES
    7. 4.7 SELF‐ASSESSMENT EXERCISES
    8. 4.8 REVIEW PROBLEMS
    9. 4.9 APPLICATIONS
    10. KEY TERMS
    11. NOTES
  11. CHAPTER 5: COVARIANCE AND CORRELATION
    1. 5.1 INTRODUCTION
    2. 5.2 COVARIANCE
    3. 5.3 CORRELATION COEFFICIENT
    4. 5.4 CONDITIONAL EXPECTATION AND VARIANCE
    5. 5.5 REGRESSION CURVES
    6. 5.6 BASIC CONCEPTS AND FORMULAS
    7. 5.7 COMPUTATIONAL EXERCISES
    8. 5.8 SELF‐ASSESSMENT EXERCISES
    9. 5.9 REVIEW PROBLEMS
    10. 5.10 APPLICATIONS
    11. KEY TERMS
  12. CHAPTER 6: IMPORTANT MULTIVARIATE DISTRIBUTIONS
    1. 6.1 INTRODUCTION
    2. 6.2 MULTINOMIAL DISTRIBUTION
    3. 6.3 MULTIVARIATE HYPERGEOMETRIC DISTRIBUTION
    4. 6.4 BIVARIATE NORMAL DISTRIBUTION
    5. 6.5 BASIC CONCEPTS AND FORMULAS
    6. 6.6 COMPUTATIONAL EXERCISES
    7. 6.7 SELF‐ASSESSMENT EXERCISES
    8. 6.8 REVIEW PROBLEMS
    9. 6.9 APPLICATIONS
    10. KEY TERMS
    11. NOTE
  13. CHAPTER 7: GENERATING FUNCTIONS
    1. 7.1 INTRODUCTION
    2. 7.2 MOMENT GENERATING FUNCTION
    3. 7.3 MOMENT GENERATING FUNCTIONS OF SOME IMPORTANT DISTRIBUTIONS
    4. 7.4 MOMENT GENERATING FUNCTIONS FOR SUM OF VARIABLES
    5. 7.5 PROBABILITY GENERATING FUNCTION
    6. 7.6 CHARACTERISTIC FUNCTION
    7. 7.7 GENERATING FUNCTIONS FOR MULTIVARIATE CASE
    8. 7.8 BASIC CONCEPTS AND FORMULAS
    9. 7.9 COMPUTATIONAL EXERCISES
    10. 7.10 SELF‐ASSESSMENT EXERCISES
    11. 7.11 REVIEW PROBLEMS
    12. 7.12 APPLICATIONS
    13. KEY TERMS
  14. CHAPTER 8: LIMIT THEOREMS
    1. 8.1 INTRODUCTION
    2. 8.2 LAWS OF LARGE NUMBERS
    3. 8.3 CENTRAL LIMIT THEOREM
    4. 8.4 BASIC CONCEPTS AND FORMULAS
    5. 8.5 COMPUTATIONAL EXERCISES
    6. 8.6 SELF‐ASSESSMENT EXERCISES
    7. 8.7 REVIEW PROBLEMS
    8. 8.8 APPLICATIONS
    9. KEY TERMS
  15. APPENDIX A: TAIL PROBABILITY UNDER STANDARD NORMAL DISTRIBUTION
  16. APPENDIX B: CRITICAL VALUES UNDER CHI‐SQUARE DISTRIBUTION
  17. APPENDIX C: STUDENT'S t‐DISTRIBUTION
  18. APPENDIX D: F‐DISTRIBUTION: 5% (LIGHTFACE TYPE) AND 1% (BOLDFACE TYPE) POINTS FOR THE F‐DISTRIBUTION
  19. APPENDIX E: GENERATING FUNCTIONS
  20. BIBLIOGRAPHY
  21. INDEX
  22. END USER LICENSE AGREEMENT

Product information

  • Title: Introduction to Probability
  • Author(s): Narayanaswamy Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
  • Release date: December 2021
  • Publisher(s): Wiley
  • ISBN: 9781118123331