Probably Not: Future Prediction Using Probability and Statistical Inference

✍ Scribed by Lawrence N. Dworsky

• Publisher: Wiley-Interscience
• Year: 2008
• Tongue: English
• Leaves: 330
• Edition: 1
• Category: Library

✦ Synopsis

An engaging, entertaining, and informative introduction to probability and prediction in our everyday livesAlthough 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 lightsWhy different gambling casino strategies ultimately offer players no advantageHow to estimate how many different birds of one species are seen on a walk through the woodsSeemingly 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 5
CONTENTS......Page 11
PREFACE......Page 15
ACKNOWLEDGMENTS......Page 19
Predicting the Future......Page 21
Rule Making......Page 23
Random Events and Probability......Page 25
The Lottery {Very Improbable Events and Large Data Sets}......Page 30
Coin Flipping {Fair Games, Looking Backwards for Insight}......Page 33
The Coin Flip Strategy that Can’t Lose......Page 39
The Prize Behind the Door {Looking Backwards for Insight, Again}......Page 40
The Checkerboard {Dealing with Only Part of the Data Set}......Page 42
The Probability Distribution Function......Page 47
Averages and Weighted Averages......Page 52
Expected Values......Page 55
The Basic Coin Flip Game......Page 57
The Standard Deviation......Page 60
The Cumulative Distribution Function......Page 68
The Confidence Interval......Page 69
Final Points......Page 70
3. BUILDING A BELL......Page 74
The One-Dimensional Random Walk......Page 87
What Probability Really Means......Page 95
Diffusion......Page 97
5. LIFE INSURANCE AND SOCIAL SECURITY......Page 102
Insurance as Gambling......Page 103
Life Tables......Page 105
Birth Rates and Population Stability......Page 110
Life Tables, Again......Page 111
Premiums......Page 114
Social Security—Sooner or Later?......Page 118
6. BINOMIAL PROBABILITIES......Page 124
The Binomial Probability Formula......Page 125
Permutations and Combinations......Page 127
Large Number Approximations......Page 129
The Poisson Distribution......Page 132
Clusters......Page 134
7. PSEUDORANDOM NUMBERS AND MONTE CARLO SIMULATIONS......Page 137
Pseudorandom Numbers......Page 138
The Middle Square PSNG......Page 139
The Linear Congruential PSNG......Page 141
A Normal Distribution Generator......Page 142
An Arbitrary Distribution Generator......Page 144
Monte Carlo Simulations......Page 146
A League of Our Own......Page 152
The Basic Coin Flip Game......Page 156
The Gantt Chart......Page 162
The “Ultimate Winning Strategy”......Page 164
The Game Show......Page 170
Parimutuel Betting......Page 174
9. TRAFFIC LIGHTS AND TRAFFIC......Page 178
Outsmarting a Traffic Light?......Page 179
Simulating Traffic Flow......Page 184
Simulation Results......Page 187
Functional Notation......Page 198
Conditional Probability......Page 203
Medical Test Results......Page 206
The Shared Birthday Problem......Page 209
11. SCHEDULING AND WAITING......Page 212
Scheduling Appointments in the Doctor’s Office......Page 213
Lunch with a Friend......Page 219
Waiting for a Bus......Page 224
12. STOCK MARKET PORTFOLIOS......Page 228
Benford’s Law......Page 235
Parrondo’s Paradox......Page 241
Simpson’s Paradox......Page 248
14. NETWORKS, INFECTIOUS DISEASE PROPAGATION, AND CHAIN LETTERS......Page 254
Degrees of Separation......Page 255
Propagation Along the Networks......Page 258
Some Other Uses of Networks......Page 262
Neighborhood Chains......Page 269
A Walk in the Woods......Page 273
A Model of Bird Flying Habits......Page 274
Spotting a Bird......Page 279
Putting It All Together......Page 281
16. STATISTICAL MECHANICS AND HEAT......Page 287
Statistical Mechanics......Page 288
Thermodynamics......Page 296
17. INTRODUCTION TO STATISTICAL ANALYSIS......Page 300
Sampling......Page 301
Sample Distributions and Standard Deviations......Page 303
Estimating Population Average from a Sample......Page 305
The Student T Distribution......Page 308
Polling Statistics......Page 310
Did a Sample Come from a Given Population?......Page 311
Chaos......Page 313
Probability in Quantum Mechanics......Page 321
INDEX......Page 327