Introduction to Probability.

Introduction to Probability.

by N. Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
Released May 2019
Publisher(s): Wiley
ISBN: 9781118123348

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Book description

An essential guide to the concepts of probability theory that puts the focus on models and applications

Introduction to Probability offers an authoritative text that presents the main ideas and concepts, as well as the theoretical background, models, and applications of probability. The authors—noted experts in the   field—include a review of problems where probabilistic models naturally arise, and discuss the methodology to tackle these problems.

A wide-range of topics are covered that include the concepts of probability and conditional probability, univariate discrete distributions, univariate continuous distributions, along with a detailed presentation of the most important probability distributions used in practice, with their main properties and applications.

Designed as a useful guide, the text contains theory of probability, de finitions, charts, examples with solutions, illustrations, self-assessment exercises, computational exercises, problems and a glossary. 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.

Written for students majoring in statistics, engineering, operations research, computer science, physics, and mathematics, Introduction to Probability: Models and Applications is an accessible text that explores the basic concepts of probability and includes detailed information on models and applications.

Table of contents

  1. Cover
  2. Dedication
  3. Preface
  4. 1 The Concept of Probability
    1. 1.1 Chance Experiments – Sample Spaces
    2. Group A
    3. 1.2 Operations Between Events
    4. Group A
    5. Group B
    6. 1.3 Probability as Relative Frequency
    7. 1.4 Axiomatic Definition of Probability
    8. Group A
    9. Group B
    10. 1.5 Properties of Probability
    11. Group A
    12. Group B
    13. 1.6 The Continuity Property of Probability
    14. Group A
    15. Group B
    16. 1.7 Basic Concepts and Formulas
    17. 1.8 Computational Exercises
    18. 1.9 Self‐assessment Exercises
    19. 1.10 Review Problems
    20. 1.11 Applications
    21. Key Terms
  5. 2 Finite Sample Spaces – Combinatorial Methods
    1. 2.1 Finite Sample Spaces with Events of Equal Probability
    2. Group A
    3. Group B
    4. 2.2 Main Principles of Counting
    5. Group A
    6. Group B
    7. 2.3 Permutations
    8. Group A
    9. Group B
    10. 2.4 Combinations
    11. Group A
    12. Group B
    13. 2.5 The Binomial Theorem
    14. Group A
    15. Group B
    16. 2.6 Basic Concepts and Formulas
    17. 2.7 Computational Exercises
    18. 2.8 Self‐Assessment Exercises
    19. 2.9 Review Problems
    20. 2.10 Applications
    21. Key Terms
  6. 3 Conditional Probability – Independent Events
    1. 3.1 Conditional Probability
    2. Group A
    3. Group B
    4. 3.2 The Multiplicative Law of Probability
    5. Group A
    6. Group B
    7. 3.3 The Law of Total Probability
    8. Group A
    9. Group B
    10. 3.4 Bayes' Formula
    11. Group A
    12. Group B
    13. 3.5 Independent Events
    14. Group A
    15. Group B
    16. 3.6 Basic Concepts and Formulas
    17. 3.7 Computational Exercises
    18. 3.8 Self‐assessment Exercises
    19. 3.9 Review Problems
    20. 3.10 Applications
    21. Key Terms
  7. 4 Discrete Random Variables and Distributions
    1. 4.1 Random Variables
    2. 4.2 Distribution Functions
    3. Group A
    4. Group B
    5. 4.3 Discrete Random Variables
    6. Group A
    7. Group B
    8. 4.4 Expectation of a Discrete Random Variable
    9. Group A
    10. Group B
    11. 4.5 Variance of a Discrete Random Variable
    12. Group A
    13. Group B
    14. 4.6 Some Results for Expectation and Variance
    15. Group A
    16. Group B
    17. 4.7 Basic Concepts and Formulas
    18. 4.8 Computational Exercises
    19. 4.9 Self‐Assessment Exercises
    20. 4.10 Review Problems
    21. 4.11 Applications
    22. Key Terms
  8. 5 Some Important Discrete Distributions
    1. 5.1 Bernoulli Trials and Binomial Distribution
    2. Group A
    3. Group B
    4. 5.2 Geometric and Negative Binomial Distributions
    5. Group A
    6. Group B
    7. 5.3 The Hypergeometric Distribution
    8. Group A
    9. Group B
    10. 5.4 The Poisson Distribution
    11. Group A
    12. Group B
    13. 5.5 The Poisson Process
    14. Group A
    15. Group B
    16. 5.6 Basic Concepts and Formulas
    17. 5.7 Computational Exercises
    18. 5.8 Self‐Assessment Exercises
    19. 5.9 Review Problems
    20. 5.10 Applications
    21. Key Terms
  9. 6 Continuous Random Variables
    1. 6.1 Density Functions
    2. Group A
    3. Group B
    4. 6.2 Distribution for a Function of a Random Variable
    5. Group A
    6. Group B
    7. 6.3 Expectation and Variance
    8. Group A
    9. Group B
    10. 6.4 Additional Useful Results for the Expectation
    11. Group A
    12. Group B
    13. 6.5 Mixed Distributions
    14. Group A
    15. Group B
    16. 6.6 Basic Concepts and Formulas
    17. 6.7 Computational Exercises
    18. 6.8 Self‐Assessment Exercises
    19. 6.9 Review Problems
    20. 6.10 Applications
    21. Key Terms
  10. CHAPTER 7: Some Important Continuous Distributions
    1. 7.1 The Uniform Distribution
    2. Group A
    3. Group B
    4. 7.2 The Normal Distribution
    5. Group A
    6. Group B
    7. 7.3 The Exponential Distribution
    8. Group A
    9. Group B
    10. 7.4 Other Continuous Distributions
    11. Group A
    12. Group B
    13. 7.5 Basic Concepts and Formulas
    14. 7.6 Computational Exercises
    15. 7.7 Self‐Assessment Exercises
    16. 7.8 Review Problems
    17. 7.9 Applications
    18. Key Terms
  11. Appendix A: Sums and Products
    1. Useful Formulas
  12. Appendix B: Distribution Function of the Standard Normal Distribution
  13. Appendix C: Simulation
  14. Appendix D: Discrete and Continuous Distributions
  15. Bibliography
    1. Other non-technical books
    2. Web sources
  16. Index
  17. End User License Agreement

Product information

  • Title: Introduction to Probability.
  • Author(s): N. Balakrishnan, Markos V. Koutras, Konstadinos G. Politis
  • Release date: May 2019
  • Publisher(s): Wiley
  • ISBN: 9781118123348