Probably Not: Future Prediction Using Probability And Statistical Inference

✍ Scribed by Lawrence N. Dworsky

• Publisher: John Wiley & Sons
• Year: 2019
• Tongue: English
• Leaves: 350
• Edition: 2nd Edition
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Cover......Page 1
Title......Page 3
Title Page......Page 5
Copyright Page......Page 6
Contents......Page 9
Acknowledgments......Page 13
About the Companion Website......Page 15
Introduction......Page 17
Predicting the Future......Page 21
Rule Making......Page 23
Random Events and Probability......Page 25
The Lottery {Very Improbable Events and Very Large Data Sets}......Page 31
Coin Flipping {Fair Games, Looking Backward for Insight}......Page 33
The Coin Flip Strategy That Can’t Lose......Page 40
The Prize Behind the Door {Looking Backward for Insight, Again}......Page 41
The Checker Board {Dealing With Only Part of the Data Set}......Page 43
Comments......Page 47
Problems......Page 48
The Probability Distribution Function......Page 51
Averages and Weighted Averages......Page 54
Expected Values (Again)......Page 57
PDF Symmetry......Page 59
Standard Deviation......Page 62
Cumulative Distribution Function......Page 71
The Confidence Interval......Page 73
Final Points......Page 74
Rehash and Histograms......Page 75
Problems......Page 82
Chapter 3 Building a Bell......Page 87
Problems......Page 103
The One-Dimensional Random Walk......Page 105
Some Subsequent Calculations......Page 109
Diffusion......Page 111
Problems......Page 115
Life Insurance......Page 119
Insurance as Gambling......Page 120
Life Tables......Page 123
Birth Rates and Population Stability......Page 128
Life Tables, Again......Page 129
Premiums......Page 131
Social Security – Sooner or Later?......Page 136
Problems......Page 141
Introduction......Page 145
The Binomial Probability Formula......Page 146
Permutations and Combinations......Page 148
Large Number Approximations......Page 150
The Poisson Distribution......Page 152
Clusters......Page 156
Problems......Page 158
Pseudorandom Numbers......Page 161
The Middle Square PRNG......Page 162
The Linear Congruential PRNG......Page 164
A Normal Distribution Generator......Page 166
An Arbitrary Distribution Generator......Page 167
Monte Carlo Simulations......Page 169
A League of Our Own......Page 172
Discussion......Page 175
Notes......Page 176
The Basic Coin Flip Game......Page 177
The “Ultimate Winning Strategy”......Page 182
Parimutuel Betting......Page 185
The Gantt Chart and a Hint of Another Approach......Page 188
Problems......Page 190
Scheduling Appointments in the Doctor’s Office......Page 193
Lunch with a Friend......Page 196
Waiting for a Bus......Page 198
Problems......Page 201
Functional Notation (Again)......Page 203
Conditional Probability......Page 205
Medical Test Results......Page 208
The Shared Birthday Problem......Page 211
Problems......Page 213
Bayes Theorem......Page 215
Multiple Possibilities......Page 218
Will Monty Hall Ever Go Away?......Page 223
Philosophy......Page 225
The Prosecutor’s Fallacy......Page 226
Continuous Functions......Page 227
Credible Intervals......Page 230
Gantt Charts (Again)......Page 231
Problems......Page 233
The Number of Locomotives Problem......Page 237
Number of Locomotives, Improved Estimate......Page 238
Decision Making......Page 240
The Lighthouse Problem......Page 243
The Likelihood Function......Page 245
The Lighthouse Problem II......Page 248
Parrondo’s Paradox......Page 249
Another Parrondo Game......Page 252
The Parrondo Ratchet......Page 255
Simpson’s Paradox......Page 256
Problems......Page 260
History......Page 263
The 1/x Distribution......Page 265
Surface Area of Countries of the World......Page 268
Goodness of Fit Measure......Page 269
Smith’s Analysis......Page 271
Problems......Page 275
Degrees of Separation......Page 277
Propagation Along the Networks......Page 281
Some Other Networks......Page 286
Neighborhood Chains......Page 287
Chain Letters......Page 289
Comments......Page 292
Sampling......Page 293
Sample Distributions and Standard Deviations......Page 296
Estimating Population Average from a Sample......Page 298
The Student-T Distribution......Page 301
A Little Reconciliation......Page 305
Correlation and Causality......Page 307
Correlation Coefficient......Page 309
Regression Lines......Page 310
Regression to the Mean......Page 311
Problems......Page 314
Introduction......Page 319
Statistical Mechanics......Page 320
(Concepts of) Thermodynamics......Page 322
Chaos......Page 327
Probability in Quantum Mechanics......Page 335
Continuous Distributions and Integrals......Page 339
Exponential Functions......Page 342
Index......Page 345
EULA......Page 350

✦ Subjects

Prediction Theory; Probabilities: Problems, Exercises, etc; Mathematical Statistics: Problems, Exercises, etc