# Introduction to Probability

John R. Baxter, University of Minnesota

Copyright Year:

Publisher: John R. Baxter

Language: English

## Formats Available

## Conditions of Use

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CC BY-SA

## Reviews

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... read more

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.

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.

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.

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.

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.

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.

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.

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.

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.

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”

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

## Table of Contents

- Contents
- Preface
- Probability and Events
- Assumptions for probability, and their consequences
- Models with continuous sample spaces
- Conditional probability
- Independence and its consequences
- Tricky little problems
- Independent sequences
- Counting
- Random variables
- Expected values, finite range case
- More properties of expected value
- Independent random variables, first applications
- Waiting times
- Random variables with countable range
- Exponential waiting times
- Moments and inequalities
- Poisson random variables
- Normal random variables and the Central Limit Theorem
- Appendices
- Bibliography
- Index

## Ancillary Material

Submit ancillary resource## About the Book

This is an introduction to probability theory, designed for self-study. It covers the same topics as the one-semester introductory courses which I taught at the University of Minnesota, with some extra discussion for reading on your own. The reasons which underlie the rules of probability are emphasized. Probability theory is certainly useful. But how does it feel to study it? Well, like other areas of mathematics, probability theory contains elegant concepts, and it gives you a chance to exercise your ingenuity, which is often fun. But in addition, randomness and probability are part of our experience in the real world, present everywhere and yet still somewhat mysterious. This gives the subject of probability a special interest.

## About the Contributors

### Author

**John R. Baxter**,
University of Minnesota