Introduction to Probability

Reviewed by Dr.Rosie Kallie, Associate Professor of Instruction, University of Texas at Arlington on 3/26/24

Comprehensiveness rating: 5 see less

Unlike many textbooks in Statistics that start with graphing, this well-written, self-study guide in Probability takes the reader on a steady journey in probability, starting with standard definitions and tools in probability. As shown in the Table of Contents, the journey begins with defining probability and events, then onward to standard probability topics such as events, sample spaces, conditional probability, independence, counting, random variables, moments, and ending with the normal distribution. Interspersed within these concise chapters are extended topics which could be classified as more advanced topics--e.g. moments and inequalities. An plausible subtitle for the text is “a theoretical approach for math-minded persons.” The material is well within the thought processes of a math-minded person who is willing to learn the mathematical notation, as it is introduced, as needed during the math journey. The index is extensive which is extremely helpful as a reference to the reading.

Content Accuracy rating: 5

In my detailed review of the text, no obvious errors were uncovered in motivation for topics, in usage of notation, in development of theory, nor in illustration of concepts. I appreciated the proverbial “dangling of a carrot” approach at the beginning of a chapter, followed by expounding on the “carrot” throughout the chapter.

Relevance/Longevity rating: 5

In the current era of “big data,” more and more disciplines of people are acquiring technical tools to understand how to interpret data. The concepts presented here are timeless tools across many professions. The book can be used as a reference, used a text for a math course, used as a guide for self-study. Readers with a calculus/math notation background may find the book especially useful. The book efficiently compartmentalizes topics into short chapters with detailed examples throughout the chapter. As an Open Educational Resource book, it appears that examples and exercises can be exchanged for more current examples, as needed.

Clarity rating: 5

Unlike the very formal tone of many technical books, the author uses a tone that is both welcoming yet thorough and knowledgeable. While using well-written prose, the author intersperses technical vocabulary with common-language parenthetical phrases, thereby enabling the reader to make key connections with the concepts.

Consistency rating: 5

The book displays a three-step process within chapter presentations: starting with a plausible context for the math concept, followed by development of the math concept, then summarize the concept with a math framework (e.g. Lemma, Theorem). Several Examples and Exercises follow the development.

Modularity rating: 5

A person versed in Probability or a new student in Probability can easily pick out the new topics, by hierarchy of the topics as shown, in order. Repeated topics, in some cases, represent an extension of a prior topic. For Example, random variables is presented in an earlier chapter, followed by several related chapters—independent random variables, poisson random variables.
The text balances out the presentation of the chapter material by providing extra detail within the chapter’s Exercises plus the Appendices. This smart planning keeps the chapters at a shorter length yet detailed in presentation.

Organization/Structure/Flow rating: 4

The author suggests that the material could easily be presented in an alternate order. The order is sufficient, with predecessor topics being shown in an appropriate place. e.g. random variables before independent random variables. To aid a non-math or new-math persons, a suggestion is to add the word “supplemental” or “advanced” to flag the appropriate follow-up chapters.

Interface rating: 4

Navigation links, via “red boxes” around various headers, are all active at the time of this review. It is relatively easy to move around within the textbook.

Grammatical Errors rating: 5

In conducting a thorough review of several chapters, no grammatical errors were detected. The text is written in prose that flows freely, without awkwardness. Do note that some repeated words were detected in only a few instances.

Cultural Relevance rating: 4

Instead of framing content toward a particular culture, the text implements people-friendly examples that may appeal to a wide swath of people. e.g. actors’ lines from the movie “The Hobbit”

Comments

I intend to use text book as a reference book for my courses.