Primer for Data Analytics and Graduate Study in Statistics

The title of this text clearly describes the motivation of the authors: To offer a primer in probability and distribution theory that they feel is needed for a career in data analytics and graduate studies in statistics. Students who enter graduate studies in Statistics come from a variety of academic backgrounds and have varying levels of exposure to the mathematics required for graduate study in Statistics. As the authors state, this text looks to bridge the gap between a general undergraduate education in a mathematically oriented field and a career-oriented graduate study in Statistics. In my opinion, the authors achieve this goal.

The contents of this text align with the standard treatment of probability and distribution theory presented in an advanced undergraduate course in Probability or a bridge course for graduate students starting a Ph.D. in Statistics or Biostatistics. After a short introduction, chapter 2 covers the basics of Probability. Chapter 3 introduces the notion of a Random Variable and chapter 4 covers various properties of Random Variables, including probability distributions for a single Random Variable. Chapter 5 covers topics related to joint probability distributions for two Random Variables. Chapter 6 covers different techniques for finding probability distributions of a function of a single random variable. Chapter 7 introduces the notion of a sampling distribution and how to obtain such a distribution. Chapter 8 finishes out the book by introducing important asymptotic statistics results such as types of convergence, Central Limit Theorems, Slutsky’s Theorem, and the Delta Method. 

There are two key features of this text that are noteworthy. First is the wealth of quality examples that the authors employ to illustrate different topics, especially in the early probability chapters. Alongside the examples, the authors employ just-in-time proofs of key theorems called mathematical moments and leading questions for the reader to ponder. Second is the high quantity and quality of exercises throughout the text. 

In my opinion, this text is a quality candidate for a primary book for an undergraduate course in Probability theory or a graduate course that introduces the basics of Statistical theory. 

Grant Innerst is an Assistant Professor of Mathematics at Shippensburg University. He is a trained statistician interested in statistics education and algebraic statistics.