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Probability: An Introduction with Statistical Applications, 2nd Edition

Book Description

Praise for the First Edition

"This is a well-written and impressively presented introduction to probability and statistics. The text throughout is highly readable, and the author makes liberal use of graphs and diagrams to clarify the theory." - The Statistician

Thoroughly updated, Probability: An Introduction with Statistical Applications, Second Edition features a comprehensive exploration of statistical data analysis as an application of probability. The new edition provides an introduction to statistics with accessible coverage of reliability, acceptance sampling, confidence intervals, hypothesis testing, and simple linear regression. Encouraging readers to develop a deeper intuitive understanding of probability, the author presents illustrative geometrical presentations and arguments without the need for rigorous mathematical proofs.

The Second Edition features interesting and practical examples from a variety of engineering and scientific fields, as well as:

  • Over 880 problems at varying degrees of difficulty allowing readers to take on more challenging problems as their skill levels increase

  • Chapter-by-chapter projects that aid in the visualization of probability distributions

  • New coverage of statistical quality control and quality production

  • An appendix dedicated to the use of Mathematica® and a companion website containing the referenced data sets

  • Featuring a practical and real-world approach, this textbook is ideal for a first course in probability for students majoring in statistics, engineering, business, psychology, operations research, and mathematics. Probability: An Introduction with Statistical Applications, Second Edition is also an excellent reference for researchers and professionals in any discipline who need to make decisions based on data as well as readers interested in learning how to accomplish effective decision making from data.

    Table of Contents

    1. Cover
    2. Title Page
    3. Copyright
    4. Dedication
    5. Preface for the First Edition
      1. Historical Note
      2. About the Text
      3. For the Instructor
    6. Preface for the Second Edition
    7. Chapter 1: Sample Spaces and Probability
      1. 1.1 Discrete Sample Spaces
      2. 1.2 Events; Axioms of Probability
      3. 1.3 Probability Theorems
      4. 1.4 Conditional Probability and Independence
      5. 1.5 Some Examples
      6. 1.6 Reliability of Systems
      7. 1.7 Counting Techniques
      8. 1.8 Chapter Review
      9. 1.9 PROBLEMS FOR REVIEW
    8. Chapter 2: Discrete Random Variables and Probability Distributions
      1. 2.1 Random Variables
      2. 2.2 Distribution Functions
      3. 2.3 Expected Values of Discrete Random Variables
      4. 2.4 Binomial Distribution
      5. 2.5 A Recursion
      6. 2.6 Some Statistical Considerations
      7. 2.7 Hypothesis Testing: Binomial Random Variables
      8. 2.8 Distribution of A Sample Proportion
      9. 2.9 Geometric and Negative Binomial Distributions
      10. 2.10 The Hypergeometric Random Variable: Acceptance Sampling
      11. 2.11 Acceptance Sampling (Continued)
      12. 2.12 The Hypergeometric Random Variable: Further Examples
      13. 2.13 The Poisson Random Variable
      14. 2.14 The Poisson Process
      15. Chapter Review
      16. Problems for Review
    9. Chapter 3: Continuous Random Variables and Probability Distributions
      1. 3.1 Introduction
      2. 3.2 Uniform Distribution
      3. 3.3 Exponential Distribution
      4. 3.4 Reliability
      5. 3.5 Normal Distribution
      6. 3.6 Normal Approximation to the Binomial Distribution
      7. 3.7 Gamma and Chi-Squared Distributions
      8. 3.8 Weibull Distribution
      9. Chapter Review
      10. Problems For Review
    10. Chapter 4: Functions of Random Variables; Generating Functions; Statistical Applications
      1. 4.1 Introduction
      2. 4.2 Some Examples of Functions of Random Variables
      3. 4.3 Probability Distributions of Functions of Random Variables
      4. 4.4 Sums of Random Variables I
      5. 4.5 Generating Functions
      6. 4.6 Some Properties of Generating Functions
      7. 4.7 Probability Generating Functions for Some Specific Probability Distributions
      8. 4.8 Moment Generating Functions
      9. 4.9 Properties of Moment Generating Functions
      10. 4.10 Sums of Random Variables—II
      11. 4.11 The Central Limit Theorem
      12. 4.12 Weak Law of Large Numbers
      13. 4.13 Sampling Distribution of the Sample Variance
      14. 4.14 Hypothesis Tests and Confidence Intervals for a Single Mean
      15. 4.15 Hypothesis Tests on Two Samples
      16. 4.16 Least Squares Linear Regression
      17. 4.17 Quality Control Chart for
      18. Chapter Review
      19. Problems for Review
    11. Chapter 5: Bivariate Probability Distributions
      1. 5.1 Introduction
      2. 5.2 Joint and Marginal Distributions
      3. 5.3 Conditional Distributions and Densities
      4. 5.4 Expected Values and the Correlation Coefficient
      5. 5.5 Conditional Expectations
      6. 5.6 Bivariate Normal Densities
      7. 5.7 Functions of Random Variables
      8. CHAPTER REVIEW
      9. PROBLEMS FOR REVIEW
    12. Chapter 6: Recursions and Markov Chains
      1. 6.1 Introduction
      2. 6.2 Some Recursions and their Solutions
      3. 6.3 Random Walk and Ruin
      4. 6.4 Waiting Times for Patterns in Bernoulli Trials
      5. 6.5 Markov Chains
      6. CHAPTER REVIEW
      7. PROBLEMS FOR REVIEW
    13. Chapter 7: Some Challenging Problems
      1. 7.1 My Socks and <img xmlns="http://www.w3.org/1999/xhtml" xmlns:epub="http://www.idpf.org/2007/ops" xmlns:m="http://www.w3.org/1998/Math/MathML" xmlns:svg="http://www.w3.org/2000/svg" xmlns:ibooks="http://vocabulary.itunes.apple.com/rdf/ibooks/vocabulary-extensions-1.0" src="images/c07-math-0001.png" alt="c07-math-001" style="vertical-align:middle;"></img>
      2. 7.2 Expected Value
      3. 7.3 Variance
      4. 7.4 Other “Socks” Problems
      5. 7.5 Coupon Collection and Related Problems
      6. 7.6 Conclusion
      7. 7.7 Jackknifed Regression and the Bootstrap
      8. 7.8 Cook's Distance
      9. 7.9 The Bootstrap
      10. 7.10 On Waldegrave's Problem
      11. 7.11 Probabilities of Winning
      12. 7.12 More than Three Players
      13. 7.13 Conclusion
      14. 7.14 On Huygen's First Problem
      15. 7.15 Changing the Sums for the Players
    14. Bibliography: Where to Learn More
    15. Appendix A: Use of Mathematica in Probability and Statistics
      1. Chapter One
      2. Chapter Two
      3. Chapter Three
      4. Chapter Four
      5. Chapter Five
      6. Chapter Six
    16. Appendix B: Answers for Odd-Numbered Exercises
      1. Chapter 1
      2. Chapter 2
      3. Chapter 3
      4. Chapter 4
      5. Chapter 5
      6. Chapter 6
    17. Appendix C: Standard Normal Distribution
      1. The Distribution Table
      2. Chi-Squared Distribution Table
    18. Index
    19. End User License Agreement