Although the book claims to be a suitable text for a first course in probability and statistics, Spanos includes in his intended audience students who have had at least a semester course in calculus. The principal problem with this claim is that, as will be shown shortly, there is much that is both omitted and that does not belong in such a text. With regard to the former, Type I and Type II errors, two-sample test of means, simple vs. composite null hypotheses, do not appear. However, the Reimann-Stieltjes integral is included but is nowhere defined, and many integration and differentiation concepts that do not appear in a typical first semester of calculus are frequently used. The above notwithstanding, the entry-requirements for accessing this book are extremely low. Linear algebra and theorem/proof methods are not used. Many theorems are stated and explained, but very few are proved formally given that the emphasis throughout is placed more on ideas and concepts. This is not to suggest that undergraduates, or even first-year graduate students, will find the book an easy read.
The book is a useful companion text, alongside, for example, John Freund, Mathematical Statistics (2001). At the University of Cambridge, UK, the two texts provide the primary references for a second year course in probability and statistics given to economists. Given the more formal exposition in Freund, students appreciate the additional insight afforded by Spanos. In addition, Spanos could be profitably assigned in tandem with Mittelhammer (1996): the former more theoretical and the latter more applied.
Chapter One: An Introduction to Empirical Modelling, introduces basic concepts, including the relation between data and a statistical model. The taxonomy of statistical information (D-dependence, M-memory, H-heterogeneity) provides a useful framework with which to understand the differences between the different types of stochastic processes.
Chapter Two: Probability Theory: a Modelling Framework, introduces basic definitions, such as continuous and discrete random variables, sets and set-theoretic operations, random experiments, events, sigma and Borel-fields, probability set functions, and a statistical space. As a prelude to reading, for example, White (1986) or econometric journals, it is much easier to learn these concepts from the present book than from, say, Shiryaev (1986), and other such texts.
Chapter Three: The Notion of a Probability Model, begins by introducing the concept of a simple random variable, which is carefully related to an event space. Well-worked examples show how to