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Introduction to Probability with Statistical Applications

Géza Schay
Publication Date: 
Number of Pages: 
[Reviewed by
Jason M. Graham
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Géza Schay’s Introduction to Probability with Statistical Applications presents the fundamentals of basic probability theory in a clear, straightforward manner. While the approach is not axiomatic nor based on measure theory, the book does provide a rigorous treatment of probability using calculus. For example, proofs of many results are given in detail but the use of linear algebra and other multi-variable mathematics is minimized. I believe that students concentrating in mathematics and related subjects will find this book readable and interesting.

The topics covered are fairly standard. The book begins with a concise but reasonably thorough treatment of the set theory and combinatorics used in basic probability theory. The notion of probability is explained via the notion of relative frequency. The bulk of the text is concerned with random variables, expectation, distributions and the other most important topics in discrete and continuous probability theory. The final chapter is dedicated to statistics which is presented as an application of the probability theory developed in the rest of the book.

I find the examples and exercises in Introduction to Probability with Statistical Applications to be particularly interesting and enjoyable. Most of them are straightforward if the reader has a solid grasp of the theory. I think that students learning the probability for the first time will get real value out of working through the examples and exercises of the text.

As one would expect from a second edition, there are very few typos or misprints in the book. In fact, Introduction to Probability with Statistical Applications is very clearly written and reading the book is enjoyable. I would certainly recommend Schay’s book as a primary textbook for an undergraduate course in calculus-based probability. Note however that, as the author states, there is more than one semester worth of material in the book. So if the desire of an instructor is to make it through both basic probability and some statistics in a single semester some very careful choices would have to be made.

Jason M. Graham is an assistant professor in the department of mathematics at the University of Scranton, Scranton, Pennsylvania. His current professional interests are in teaching applied mathematics and mathematical biology, and collaborating with biologists specializing in the collective behavior of groups of organisms.

See the table of contents in the publisher's webpage.