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Applied Probability

Models and Intuition


by Arnold I. Barnett

Dynamic Ideas, Belmont, Massachusetts, 2015.

ISBN: 978-0-9899108-7-3

Applied Probability: Models and Intuition is an introductory textbook in Probability, written from the viewpoint of Applied Mathematics. Under that perspective, theoretical rigor is not denigrated, but the book puts a high premium on offering an intuitive overview of key theorems as well as clear evidence of their usefulness. Beyond teaching specific methods, the book strives to create real comfort with the underlying notions of probabilistic thinking. Grasping such ideas is essential if they are to be used with competence and confidence.


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A  primary objective of the book is to demonstrate that Probability and Statistics are, more than anything, just crystallizations of common sense. The reader should come away from each lesson understanding not only how a result was obtained but also why the outcome is plausible

The book is intended to a support a one-semester course in Applied Probability, though it could undergird a one-quarter course if some topics are skipped. (Topics that are not necessary for subsequent material (e.g., z -transforms for discrete random variables) are identified when they are introduced.) The book strives to be suitable for both undergraduate and graduate students who concentrate in Engineering, Business, the Natural Sciences, and the Social Sciences, as well as for Math majors with an interest in applications.

Solution Manual

A solution manual that includes solutions to all exercises in the book is available to qualified instructors. Interested parties should contact the publisher at to obtain the solution manual.

Praises for Applied Probability

“A  fantastic book by one of the greatest teachers of all time!” – Professor Jonathan Caulkins, Carnegie-Mellon University

“A  probability text with more intuitive explanations and such a breadth of real world examples does not exist. This book is both approachable and rigorous.” - Professor David Czerwinski, San Jose State University

“I love this book! It presents applied probability in a friendly, sometimes folksy way that at the same time is precise, clear and well-structured. It is not intimidating, and Professor Barnett has a unique sense of humor that keeps us smiling and entertained, all the time focused on real-world applications as a way of learning the theory. The reader eagerly anticipates each ‘Barnett application’, making learning probability a pure joy.” - Professor Richard C. Larson, MIT

“Offering much more than math, this winning book teaches you to think with probability. Developing the intuition required to understand and recast real world situations in probabilistic terms is a crucial skill in itself, and I can think of no other text that does more in this regard.” - Professor Edward Kaplan, Yale University

“A  unique and wonderful book, with examples and exercises that are brilliant. They reinforce basic concepts, help students to adapt tools and techniques to new situations (no ‘cookie cutter’ problems here), and reveal how probability and statistics pervade our lives.” - Professor Robert Shumsky, Dartmouth College

About The Author

Arnold I. Barnett is George Eastman Professor of Management Science and Professor of Statistics at MIT’s Sloan School of Management. He has received the President’s Award and Expository Writing Award from INFORMS, and the President’s Citation from the Flight Safety Foundation for “truly outstanding contributions with respect to safety.”  At MIT, Professor Barnett has been honored by students 13 times for his outstanding teaching of Probability and Statistics.