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Probably Not: Future Prediction Using Probability and Statistical Inference

ISBN: 978-0-470-18401-1
328 pages
April 2008
Probably Not: Future Prediction Using Probability and Statistical Inference  (0470184019) cover image
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.

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Introduction.

1. An Introduction to Probability.

Predicting The Future.

Rule Making.

Random Events and Probability.

The Lottery {Very Improbable Events and Large Data Sets}.

Coin Flipping {Fair Games, Looking Backwards For Insight}.

The Coin Flip Strategy That Can’t Lose.

The Prize Behind The Door {Looking Backwards For Insight, Again}.

The Checker Board {Dealing With Only Part Of The Data Set}.

2. Probability Distribution Functions And Some Basics.

The Probability Distribution Function.

Averages And Weighted Averages.

Expected Values.

The Basic Coin Flip Game.

The Standard Deviation.

The Cumulative Distribution Function.

The Confidence Interval.

Final Points.

3. Building a Bell.

4. Random Walks.

The One Dimensional Random Walk.

What Probability Really Means.

Diffusion.

5. Life Insurance and Social Security.

Insurance as Gambling.

Life Tables.

Birth Rates and Population Stability.

Life Tables, Again.

Premiums.

Social Security - Sooner Or Later?.

6. Binomial Probabilities.

The Binomial Probability Formula.

Permutations And Combinations.

Large Number Approximations.

The Poisson Distribution.

Disease Clusters.

Clusters.

7. Pseudorandom Numbers and Monte Carlo Simulations.

Pseudorandom Numbers.

The Middle Square PSNG.

The Linear Congruential PSNG.

A Normal Distribution Generator.

An Arbitrary Distribution Generator.

Monte Carlo Simulations.

A League Of Our Own.

8. Some Gambling Games In Detail.

The Basic Coin Flip Game.

The Gantt Chart.

The Ultimate "Winning Strategy".

The Game Show.

Parimutuel Betting.

9. Traffic Lights And Traffic.

Outsmarting A Traffic Light?.

Many Lights And Many Cars.

Simulating Traffic Flow - The Simulation.

Simulation Results.

10. Combined And Conditional Probabilities.

Functional Notation.

Conditional Probability.

Medical Test Results.

The Shared Birthday Problem.

11. Scheduling And Waiting.

Scheduling Appointments In The Doctor’s Office.

Lunch With A Friend.

Waiting For A Bus.

12. Stock Market Portfolios.

13. Benford, Parrondo and Simpson.

Benford’s Law.

Parrondo’s Paradox.

Simpson’s Paradox.

14. Networks, Infectious Disease Propagation and Chain Letters.

Degrees Of Separation.

Propagation Along Networks.

Some Other Uses Of Networks.

Neighborhood Chains.

15. Bird Counting.

A Walk In The Woods.

A Model Of Bird Flying Habits.

Spotting A Bird.

Putting It All Together.

16. Statistical Mechanics And Heat.

Statistical Mechanics.

Thermodynamics.

17. Introduction To Statistical Analysis.

Sampling.

Sample Distributions and Standard Deviations.

Estimating Population Average From A Sample.

The Student-T Distribution.

Polling Statistics.

Did A Sample Come From A Given Population?.

18. Chaos and Quanta.

Chaos.

Probability In Quantum Mechanics.

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Lawrence N. Dworsky, PhD, is a former corporate research lab director at Motorola, Inc., where he was also a member of the Science Advisory Board. He has also served as a consultant to the Defense Advanced Research Projects Agency (DARPA), Littelfuse Corp., and HRL Laboratories, LLC. A Fellow of the Institute of Electrical and Electronic Engineers, Dr. Dworsky has held academic positions at Columbia University, Northern Illinois University, and Florida Atlantic University.

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"The book is a very good tool for students and specialists in different areas who do not like advanced statistics, but are obliged to understand, a least partly, the process of decision making." (International Statistical Review, December 2008)

"The fact that Dworsky uses examples from many fields, and discusses topics not usually covered in beginning course, may also increase student interest in pursuing statistics at a more advanced level." (MAA Reviews, July 2008)

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