Probably Not: Future Prediction Using Probability and Statistical Inference, 2nd Edition
by Lawrence N. Dworsky (Author)

About the Author
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.

About this book
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 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.

Brief contents
1 An Introduction to Probability 5
    Predicting the Future 5
    Rule Making 7
    Random Events and Probability 9
    The Lottery {Very Improbable Events and Very Large Data Sets} 15
    Coin Flipping {Fair Games, Looking Backward for Insight} 17
    The Coin Flip Strategy That Can’t Lose 24
    The Prize Behind the Door {Looking Backward for Insight, Again} 25
    The Checker Board {Dealing With Only Part of the Data Set} 27
    Comments 31
    Problems 32
2 Probability Distribution Functions and Some Math Basics 35
    The Probability Distribution Function 35
    Averages and Weighted Averages 38
    Expected Values (Again) 41
    The Basic Coin Flip Game 43
    PDF Symmetry 43
    Standard Deviation 46
    Cumulative Distribution Function 55
    The Confidence Interval 57
    Final Points 58
    Rehash and Histograms 59
    Problems 66
3 Building a Bell 71
    Problems 87
4 Random Walks 89
    The One‐Dimensional Random Walk 89
    Some Subsequent Calculations 93
    Diffusion 95
    Problems 99
5 Life Insurance 103
    Introduction 103
    Life Insurance 103
    Insurance as Gambling 104
    Life Tables 107
    Birth Rates and Population Stability 112
    Life Tables, Again 113
    Premiums 115
    Social Security – Sooner or Later? 120
    Problems 125
6 The Binomial Theorem 129
    Introduction 129
    The Binomial Probability Formula 130
    Permutations and Combinations 132
    Large Number Approximations 134
    The Poisson Distribution 136
    Disease Clusters 140
    Clusters 140
    Problems 142
7 Pseudorandom Numbers and Monte Carlo Simulations 145
    Random Numbers and Simulations 145
    Pseudorandom Numbers 145
    The Middle Square PRNG 146
    The Linear Congruential PRNG 148
    A Normal Distribution Generator 150
    An Arbitrary Distribution Generator 151
    Monte Carlo Simulations 153
    A League of Our Own 156
    Discussion 159
    Notes 160
8 Some Gambling Games in Detail 161
    The Basic Coin Flip Game 161
    The “Ultimate Winning Strategy” 166
    Parimutuel Betting 169
    The Gantt Chart and a Hint of Another Approach 172
    Problems 174
9 Scheduling and Waiting 177
    Introduction 177
    Scheduling Appointments in the Doctor’s Office 177
    Lunch with a Friend 180
    Waiting for a Bus 182
    Problems 185
10 Combined and Conditional Probabilities 187
    Introduction 187
    Functional Notation (Again) 187
    Conditional Probability 189
    Medical Test Results 192
    The Shared Birthday Problem 195
    Problems 197
11 Bayesian Statistics 199
    Bayes Theorem 199
    Multiple Possibilities 202
    Will Monty Hall Ever Go Away? 207
    Philosophy 209
    The Prosecutor’s Fallacy 210
    Continuous Functions 211
    Credible Intervals 214
    Gantt Charts (Again) 215
    Problems 217
12 Estimation Problems 221
    The Number of Locomotives Problem 221
    Number of Locomotives, Improved Estimate 222
    Decision Making 224
    The Lighthouse Problem 227
    The Likelihood Function 229
    The Lighthouse Problem II 232
13 Two Paradoxes 233
    Introduction 233
    Parrondo’s Paradox 233
    Another Parrondo Game 236
    The Parrondo Ratchet 239
    Simpson’s Paradox 240
    Problems 244
14 Benford’s Law 247
    Introduction 247
    History 247
    The 1/x Distribution 249
    Surface Area of Countries of the World 252
    Goodness of Fit Measure 253
    Smith’s Analysis 255
    Problems 259
15 Networks, Infectious Diseases, and Chain Letters 261
    Introduction 261
    Degrees of Separation 261
    Propagation Along the Networks 265
    Some Other Networks 270
    Neighborhood Chains 271
    Chain Letters 273
    Comments 276
16 Introduction to Frequentist Statistical Inference 277
    Introduction 277
    Sampling 277
    Sample Distributions and Standard Deviations 280
    Estimating Population Average from a Sample 282
    The Student‐T Distribution 285
    Did Sample Come from a Given Population? 289
    A Little Reconciliation 289
    Correlation and Causality 291
    Correlation Coefficient 293
    Regression Lines 294
    Regression to the Mean 295
    Problems 298
17 Statistical Mechanics and Thermodynamics 303
    Introduction 303
    Statistical Mechanics 304
    (Concepts of) Thermodynamics 306
18 Chaos and Quanta 311
    Introduction 311
    Chaos 311
    Probability in Quantum Mechanics 319
Appendix 323
Index 329

Pages: 352 pages
Publisher: Wiley; 2 edition (September 4, 2019)
Language: English
ISBN-10: 1119518105
ISBN-13: 978-1119518105