Probably Not: Future Prediction Using Probability And Statistical Inference

Description

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. 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