Missing picture

Probably Not

John Wiley..... 2019


Table of Contents

Chapter Title Page
Introduction
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1An Introduction To Probability 5
Predicting The Future5
Rule Making 7
Random Events and Probability 9
The Lottery {Very Improbable Events and Large Data Sets} 15
Coin Flipping {Fair Games, Looking Backward For Insight} 17
The Coin Flipping Strategy That Can't Lose 24
The Prize Behind The Door {Looking Backward For Insight, Again} 25
The Checkerboard {Dealing With Only Part of the Data Set} 27
Comments 31
*Problems 32
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2Probability Distribution Functions and Some Basics 35
The Probability Distribution Function 35
Average and Weighted Averages 38
Expected Values 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
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3Building A Bell 71
*Problems 87
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4Random Walks 89
The One Dimensional Random Walk 89
Some Subsequent Calculations 93
Diffusion 95
*Problems 99
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5Life 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 124
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6The Binomial Theorem 129
Introduction 129
The Binomial Probability Formula 130
Permutations And Combinations 132
Large Number Approximations 134
The Poisson Equation 136
Disease Clusters 140
Clusters 140
*Problems 142
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7Pseudorandom Numbers and Monte Carlo Simulations 145
Random Numbers and Simulations 145
Pseudorandom Numbers 145
The Middle Squares PSNG 146
The Linear Congruential PSNG 148
A Normal Distribution Generator 150
An Arbitrary Distribution Generator 151
Monte Carlo Simulations 153
A League Of Our Own 156
Discussion 159
*Problems 160
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8Some Gambling Games In Detail 161
The Basic Coin Flip Game 161
"Ultimate Winning Strategy" 166
Parimutuel Betting 169
*The Gantt Chart and a Hint of Another Approach 172
*Problems 174
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9Scheduling and Waiting 177
Introduction 177
Scheduling Appointments in the Doctor's Office 177
Lunch With A Friend 180
Waiting For A Bus 182
*Problems 183
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10Combined And Conditional Probabilities 187
Introduction 187
Functional Notation (Again) 187
Conditional Probability 189
Medical Test Results 192
The Shared Birthday Problem 195
*Problems 197
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11Bayesian 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
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12Estimation *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
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13Two Paradoxes 233
Introduction 233
Porrondo's Paradox 233
Another Parrondo Game 236
The Parrondo Ratchet 239
Simpson's Paradox 240
*Problems 244
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14Benford'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'snalysis 255
*Problems 259
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15Networks, 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
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16Introduction To Frequentist Statistical Inference 277
Introduction 277
Sampling 277
Sample Distributions And Standard Deviations 280
Estimating Population Average From A Sample 280
The Student T Distribution 285
*Did A Sample Come From A Given Population? 289
*A Little Reconciliation 289
*Correlation and Causality 291
*Correlation Coefficient 283
*Regression Lines 294
*Regression to the Mean 296
*Problems 298
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17Statistical Mechanics And ThermodynamicsS 303
Introduction 303
Statistical Mechanics 304
(Concepts of) Thermoydynamics 306
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18Chaos And Quanta 311
Introduction 311
Chaos 311
Probability In Quantum Mechanics 319
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*Appendix 323
Index 329
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*New or Significantly Changed from 1st Edition
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