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
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