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Probability: For the Enthusiastic Beginner

David Morin
Self Published
Publication Date: 
Number of Pages: 
[Reviewed by
Mark Bollman
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When I was first assigned to teach a stand-alone probability course, some 25 years ago, it was a challenge to find a suitable textbook.  I was looking for a book at a level that involved some calculus but wasn’t fully reliant on integration to explore this subject, for the students in my class had seen some calculus but weren’t fully-versed in some of the aspects of the subject that are useful in probability. For example, finding the expected value of an exponential random variable calls for integration by parts, but many of my students had only completed Calculus I.  Some of this missing calculus could be backfilled, but at the cost of taking time and energy away from the study of probability.
Times have changed: there are now several good probability textbooks on the market, and Probability for the Enthusiastic Beginner has a rightful place among the best of them.  Calculus is largely confined to exercises and exercises involving calculus are clearly labeled, but this does not seriously limit the mathematical intensity of the material.  We find all the usual examples–the birthday problem and several variations, Monty Hall, the prosecutor’s fallacy, and the boy/girl problem among them–and the discussion of these and other problems is as compelling a treatment of the subjects as is the mathematics.  Later topics carry this same balance between English and mathematics, to the reader’s considerable benefit.
When reading probability textbooks, I always try to find something different that’s not among the standard probability topics.  Here, and of particular interest,  it’s the final chapter, on correlation and regression.  These topics typically sit much closer to the statistics side of “probability and statistics” when those two subfields are run together as though they were one, yet it is appropriate for a probability text to address these related ideas and illustrate the important role that randomness plays in assessing correlation among variables and the value–if any–of a linear relationship.  This chapter is a nice way to cap off a fine text.  Randomness has consequences, and Probability for the Enthusiastic Beginner does an excellent job of describing and analyzing those consequences.

Mark Bollman is a professor and chair of the Department of Mathematics and Computer Science at Albion College.