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