Probably Not, 2nd Edition

Book description

A revised edition that explores random numbers, probability, and statistical inference at an introductory mathematical level

Written in an engaging and entertaining manner, the revised and updated second edition of Probably Not continues to offer an informative guide to probability and prediction. The expanded second edition contains problem and solution sets. In addition, the book’s illustrative examples reveal how we are living in a statistical world, what we can expect, what we really know based upon the information at hand and explains when we only think we know something.

The author introduces the principles of probability and explains probability distribution functions. The book covers combined and conditional probabilities and contains a new section on Bayes Theorem and Bayesian Statistics, which features some simple examples including the Presecutor’s Paradox, and Bayesian vs. Frequentist thinking about statistics. New to this edition is a chapter on Benford’s Law that explores measuring the compliance and financial fraud detection using Benford’s Law. This book:

  • Contains relevant mathematics and examples that demonstrate how to use the concepts presented
  • Features a new chapter on Benford’s Law that explains why we find Benford’s law upheld in so many, but not all, natural situations
  • Presents updated Life insurance tables
  • Contains updates on the Gantt Chart example that further develops the discussion of random events
  • Offers a companion site featuring solutions to the problem sets within the book

Written for mathematics and statistics students and professionals, the updated edition of Probably Not: Future Prediction Using Probability and Statistical Inference, Second Edition combines the mathematics of probability with real-world examples.

LAWRENCE N. DWORSKY, PhD, is a retired Vice President of the Technical Staff and Director of Motorola’s Components Research Laboratory in Schaumburg, Illinois, USA. He is the author of Introduction to Numerical Electrostatics Using MATLAB from Wiley.

Table of contents

  1. Cover
  2. Acknowledgments
  3. About the Companion Website
  4. Introduction
  5. 1 An Introduction to Probability
    1. Predicting the Future
    2. Rule Making
    3. Random Events and Probability
    4. The Lottery {Very Improbable Events and Very Large Data Sets}
    5. Coin Flipping {Fair Games, Looking Backward for Insight}
    6. The Coin Flip Strategy That Can't Lose
    7. The Prize Behind the Door {Looking Backward for Insight, Again}
    8. The Checker Board {Dealing With Only Part of the Data Set}
    10. Problems
  6. 2 Probability Distribution Functionsand Some Math Basics
    1. The Probability Distribution Function
    2. Averages and Weighted Averages
    3. Expected Values (Again)
    4. The Basic Coin Flip Game
    5. PDF Symmetry
    6. Standard Deviation
    7. Cumulative Distribution Function
    8. The Confidence Interval
    9. Final Points
    10. Rehash and Histograms
    11. Problems
  7. 3 Building a Bell
    1. Problems
  8. 4 Random Walks
    1. The One‐Dimensional Random Walk
    2. Some Subsequent Calculations
    3. Diffusion
    4. Problems
  9. 5 Life Insurance
    1. Introduction
    2. Life Insurance
    3. Insurance as Gambling
    4. Life Tables
    5. Birth Rates and Population Stability
    6. Life Tables, Again
    7. Premiums
    8. Social Security – Sooner or Later?
    9. Problems
  10. 6 The Binomial Theorem
    1. Introduction
    2. The Binomial Probability Formula
    3. Permutations and Combinations
    4. Large Number Approximations
    5. The Poisson Distribution
    6. Disease Clusters
    7. Clusters
    8. Problems
  11. 7 Pseudorandom Numbers and Monte Carlo Simulations
    1. Random Numbers and Simulations
    2. Pseudorandom Numbers
    3. The Middle Square PRNG
    4. The Linear Congruential PRNG
    5. A Normal Distribution Generator
    6. An Arbitrary Distribution Generator
    7. Monte Carlo Simulations
    8. A League of Our Own
    9. Discussion
  12. 8 Some Gambling Games in Detail
    1. The Basic Coin Flip Game
    2. The “Ultimate Winning Strategy”
    3. Parimutuel Betting
    4. The Gantt Chart and a Hint of Another Approach
    5. Problems
  13. 9 Scheduling and Waiting
    1. Introduction
    2. Scheduling Appointments in the Doctor's Office
    3. Lunch with a Friend
    4. Waiting for a Bus
    5. Problems
  14. 10 Combined and Conditional Probabilities
    1. Introduction
    2. Functional Notation (Again)
    3. Conditional Probability
    4. Medical Test Results
    5. The Shared Birthday Problem
    6. Problems
  15. 11 Bayesian Statistics
    1. Bayes Theorem
    2. Multiple Possibilities
    3. Will Monty Hall Ever Go Away?
    4. Philosophy
    5. The Prosecutor's Fallacy
    6. Continuous Functions
    7. Credible Intervals
    8. Gantt Charts (Again)
    9. Problems
  16. 12 Estimation Problems
    1. The Number of Locomotives Problem
    2. Number of Locomotives, Improved Estimate
    3. Decision Making
    4. The Lighthouse Problem
    5. The Likelihood Function
    6. The Lighthouse Problem II
  17. 13 Two Paradoxes
    1. Introduction
    2. Parrondo's Paradox
    3. Another Parrondo Game
    4. The Parrondo Ratchet
    5. Simpson's Paradox
    6. Problems
  18. 14 Benford's Law
    1. Introduction
    2. History
    3. The 1/x Distribution
    4. Surface Area of Countries of the World
    5. Goodness of Fit Measure
    6. Smith's Analysis
    7. Problems
  19. 15 Networks, Infectious Diseases, and Chain Letters
    1. Introduction
    2. Degrees of Separation
    3. Propagation Along the Networks
    4. Some Other Networks
    5. Neighborhood Chains
    6. Chain Letters
  20. 16 Introduction to Frequentist Statistical Inference
    1. Introduction
    2. Sampling
    3. Sample Distributions and Standard Deviations
    4. Estimating Population Average from a Sample
    5. The Student‐T Distribution
    6. Did a Sample Come from a Given Population?
    7. A Little Reconciliation
    8. Correlation and Causality
    9. Correlation Coefficient
    10. Regression Lines
    11. Regression to the Mean
    12. Problems
  21. 17 Statistical Mechanics and Thermodynamics
    1. Introduction
    2. Statistical Mechanics
    3. (Concepts of) Thermodynamics
  22. 18 Chaos and Quanta
    1. Introduction
    2. Chaos
    3. Probability in Quantum Mechanics
  23. Appendix
    1. Introduction
    2. Continuous Distributions and Integrals
    3. Exponential Functions
  24. Index
  25. End User License Agreement

Product information

  • Title: Probably Not, 2nd Edition
  • Author(s): Lawrence N. Dworsky
  • Release date: September 2019
  • Publisher(s): Wiley
  • ISBN: 9781119518105