Probably Not, 2nd Edition

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}
   9. Comments
   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
    7. Comments
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