Essential Statistics

ting. In addition, independence, covariance, conditioning, and functions of several random variables (such as sums) are discussed. Chapter 7 contains the ideas and techniques of generating functions, in particular probability and moment generators. This chapter concludes with applications to the central limit theorem, branching processes, and random walks. As one would hope in a book designed for self-study, there are many worked-out examples. Each section concludes with a set of “exercises,” and each chapter with a set of “problems.” The exercises are fairly routine, involving the ideas and techniques in nearby text. The problems are less routine, and often involve new settings and ideas from further aŽ eld. The book also includes hints and solutions for most of the exercises and problems. The stated prerequisites (in the preface) for the book are “common sense, practical arithmetic, and some bits of elementary algebra.” However, integrals, inŽ nite series, and limits appear in Chapter 4, derivatives and improper integrals in Chapter 5, and double integrals in Chapter 6. To aid the reader whose background consist of only elementary algebra, the author has provided a number of chapter appendices wherein one Ž nds, for example, calculus of one and two variables (two pages), inŽ nite series (one page), and double integrals in rectangular and polar coordinates (two pages). I think most American readers (the author is at the University of Oxford) would be well advised to have some formal training in calculus of one and several variables prior to using this text, and treat the above mentioned chapter appendixes as review material. Comparable books on my shelves include Chung (1974), Hoel, Port, and Stone (1971), Ross (1984), and Thorp (1966). Of these, Stirzaker is most similar to Ross (1984). I agree with the author that the book is written in “an informal tutorial style.” I would not hesitate to recommend it for independent study to a colleague in mathematics or one of the natural or social sciences (assuming a working knowledge of calculus). I think the text would also work well in an independent study course with a bright, highly motivated, well-prepared undergraduate student. I would also consider it as the text for a onesemester junior/ senior level course in probability.