Probably Not: Future Prediction Using Probability and Statistical Inference

✍ Scribed by Lawrence N. Dworsky

• Publisher: Wiley-Interscience
• Year: 2008
• Tongue: English
• Leaves: 328
• Category: Library

✦ Synopsis

An engaging, entertaining, and informative introduction to probability and prediction in our everyday lives

Although Probably Not deals with probability and statistics, it is not heavily mathematical and is not filled with complex derivations, proofs, and theoretical problem sets. This book unveils the world of statistics through questions such as what is known based upon the information at hand and what can be expected to happen. While learning essential concepts including ''the confidence factor'' and ''random walks,'' readers will be entertained and intrigued as they move from chapter to chapter. Moreover, the author provides a foundation of basic principles to guide decision making in almost all facets of life including playing games, developing winning business strategies, and managing personal finances.

Much of the book is organized around easy-to-follow examples that address common, everyday issues such as:

• How travel time is affected by congestion, driving speed, and traffic lights

• Why different gambling casino strategies ultimately offer players no advantage

• How to estimate how many different birds of one species are seen on a walk through the woods

Seemingly random events—coin flip games, the Central Limit Theorem, binomial distributions and Poisson distributions, Parrando's Paradox, and Benford's Law—are addressed and treated through key concepts and methods in probability. In addition, fun-to-solve problems including ''the shared birthday'' and ''the prize behind door number one, two, or three'' are found throughout the book, which allow readers to test and practice their new probability skills. Requiring little background knowledge of mathematics, readers will gain a greater understanding of the many daily activities and events that involve random processes and statistics.

Combining the mathematics of probability with real-world examples, Probably Not is an ideal reference for practitioners and students who would like to learn more about the role of probability and statistics in everyday decision making.

✦ Table of Contents

PROBABLY NOT......Page 3
CONTENTS......Page 9
PREFACE......Page 13
ACKNOWLEDGMENTS......Page 17
Predicting the Future......Page 19
Rule Making......Page 21
Random Events and Probability......Page 23
The Lottery {Very Improbable Events and Large Data Sets}......Page 28
Coin Flipping {Fair Games, Looking Backwards for Insight}......Page 31
The Coin Flip Strategy that Can’t Lose......Page 37
The Prize Behind the Door {Looking Backwards for Insight, Again}......Page 38
The Checkerboard {Dealing with Only Part of the Data Set}......Page 40
The Probability Distribution Function......Page 45
Averages and Weighted Averages......Page 50
Expected Values......Page 53
The Basic Coin Flip Game......Page 55
The Standard Deviation......Page 58
The Cumulative Distribution Function......Page 66
The Confidence Interval......Page 67
Final Points......Page 68
3. BUILDING A BELL......Page 72
The One-Dimensional Random Walk......Page 85
What Probability Really Means......Page 93
Diffusion......Page 95
5. LIFE INSURANCE AND SOCIAL SECURITY......Page 100
Insurance as Gambling......Page 101
Life Tables......Page 103
Birth Rates and Population Stability......Page 108
Life Tables, Again......Page 109
Premiums......Page 112
Social Security—Sooner or Later?......Page 116
6. BINOMIAL PROBABILITIES......Page 122
The Binomial Probability Formula......Page 123
Permutations and Combinations......Page 125
Large Number Approximations......Page 127
The Poisson Distribution......Page 130
Clusters......Page 132
7. PSEUDORANDOM NUMBERS AND MONTE CARLO SIMULATIONS......Page 135
Pseudorandom Numbers......Page 136
The Middle Square PSNG......Page 137
The Linear Congruential PSNG......Page 139
A Normal Distribution Generator......Page 140
An Arbitrary Distribution Generator......Page 142
Monte Carlo Simulations......Page 144
A League of Our Own......Page 150
The Basic Coin Flip Game......Page 154
The Gantt Chart......Page 160
The “Ultimate Winning Strategy”......Page 162
The Game Show......Page 168
Parimutuel Betting......Page 172
9. TRAFFIC LIGHTS AND TRAFFIC......Page 176
Outsmarting a Traffic Light?......Page 177
Simulating Traffic Flow......Page 182
Simulation Results......Page 185
Functional Notation......Page 196
Conditional Probability......Page 201
Medical Test Results......Page 204
The Shared Birthday Problem......Page 207
11. SCHEDULING AND WAITING......Page 210
Scheduling Appointments in the Doctor’s Office......Page 211
Lunch with a Friend......Page 217
Waiting for a Bus......Page 222
12. STOCK MARKET PORTFOLIOS......Page 226
Benford’s Law......Page 233
Parrondo’s Paradox......Page 239
Simpson’s Paradox......Page 246
14. NETWORKS, INFECTIOUS DISEASE PROPAGATION, AND CHAIN LETTERS......Page 252
Degrees of Separation......Page 253
Propagation Along the Networks......Page 256
Some Other Uses of Networks......Page 260
Neighborhood Chains......Page 267
A Walk in the Woods......Page 271
A Model of Bird Flying Habits......Page 272
Spotting a Bird......Page 277
Putting It All Together......Page 279
16. STATISTICAL MECHANICS AND HEAT......Page 285
Statistical Mechanics......Page 286
Thermodynamics......Page 294
17. INTRODUCTION TO STATISTICAL ANALYSIS......Page 298
Sampling......Page 299
Sample Distributions and Standard Deviations......Page 301
Estimating Population Average from a Sample......Page 303
The Student T Distribution......Page 306
Polling Statistics......Page 308
Did a Sample Come from a Given Population?......Page 309
Chaos......Page 311
Probability in Quantum Mechanics......Page 319
INDEX......Page 325

✦ Subjects

Математика;Теория вероятностей и математическая статистика;Теория вероятностей;