“Probability Theory” and “Statistics” are two different subjects, the first a part of mathematics and the second a different field entirely. Usually, however, in a first course the two topics are treated together. This is perhaps because of the natural application of results from probability theory in justifying statistical procedures. It seems that many universities offer a course in “probability with statistical applications” being offered to students in mathematics, including engineering, physics and computer sciences.
Motivated by this point of view, the author of the book under review has clearly written with such a course in mind. The book covers a number of selected topics in probability suitable for a semester course in the subject, and contains chapters studying statistical applications of the theory. The approach is based on giving various examples and exercises, rather than on detailed explanations of concepts. For this reason, the reader does not need a deep knowledge of calculus, at least for the early chapters. Of course, later chapters include some proofs, mainly based on calculus and linear algebra computations.
The author presented main results and formulas in boxed displays, allowing undergraduate readers to review the main lines of previous pages easily. The selection of main topics is similar to what one finds in the classic books. Thus, it seems that the book won’t be very fruitful for research purposes.
I recommend this book for first and second semester of an undergraduate course in probability and statistics. In addition, instructors teaching such a course will find some very good examples and exercises for classroom use.
Mehdi Hassani is a faculty member at the Department of Mathematics, Zanjan University, Iran. His field of interest is Elementary, Analytic and Probabilistic Number Theory.
Preface to the Second Edition.- Preface.- Probability Space.- Random Variables.- Binomial and Poisson Random Variables.- Limit Theorems.- Estimation and Hypothesis Testing.- Linear Regression.- Moment Generating Functions and Sums of Independent Random Variables.- Transformations of Random Variables and Random Vectors.- Finding and Comparing Estimators.- Multiple Linear Regression.- Further Reading.- Common Distributions.- Normal Table.- Student Table.- Chi-Square Table.- Index.