Probability tales

Author(s): 
Charles M. Grinstead, William P. Peterson, J. Laurie Snell
Publisher: 
AMS
Year: 
2011
ISBN: 
978-0-8218-5261-3
Short description: 

Probability tales explores four real-world topics through the lens of probability theory. The authors assume as a prerrequisite the basic concepts in probability theory and focus, in an expository style, on four specific subjects: streaks, the stock market, lotteries and fingerprinting.

MSC main category: 
60 Probability theory and stochastic processes
MSC category: 
60-01
Review: 

Probability is a subject well-considered by most people outside the mathematical community. As mathematicians, we know that research in algebra or geometry leads us to a better understanding of the physical world, and that sometimes amazing connections or applications appear for mathematical theories which have been already developed. Probability arises in many places in our daily life: sports, economy, design.. and yet many textbooks usually introduce the same collection of examples when they try to explain the basic notions in probability.

Probability tales tries to solve this problem by explaning probability theory applied to four different real-world topics, one per chapter. More concretely, the first chapter is devoted to streakiness: cold or hot streaks occur in different sports and the authors explain how different mathematical models (Bernouilli, Markov chains...) are used to fit the existent data and to explain these success and failure runs in baseball, basketball, tennis... The second chapter is focused on the stock market, and on how the variations in the prize of a stock can be modelled, from the basics to more complicated models. A nice exposition on Powerball lottery and the funny behaviour of lottery players occupies chapter 3, and a historical evolution of fingerprinting and its relationship with probability is the topic of chapter four.

The style is informal and the topics are not presented as in an standard textbook: the book is a a collection of four independent short essays on probability, which can be read easily avoiding technicalities. However, the details in each topic are gathered in short appendices after each chapter, and several references to research articles are provided.

To get a good grip on the text, the prerrequisites are probability and calculus at the level covered in a basic undergraduate course. The authors point out the possible use of the text as a good complement to an ordinary undergraduate textbook: Probability tales explains some basic notions (hypothesis tests, p-values, distributions)put into context, so it might serve well to this purpose.

Reviewer: 
Javier Martinez
Affiliation: 
Universidad Complutense de Madrid, Spain

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