Elementary Applications of Probability Theory. by H. C. TuckwellReview by: Jacky WilsonJournal of the Royal Statistical Society. Series D (The Statistician), Vol. 40, No. 1 (1991), p. 115Published by: Wiley for the Royal Statistical SocietyStable URL: http://www.jstor.org/stable/2348239 .

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Book Reviews 115

so that cross-referencing them is awkward. Overall, the book does not meet my hopes but some of the chapters may be useful as background reading for teaching statistics.

SIMON DAY Lilly Research Centre Ltd, Surrey, UK

BARBER, T. X. (1976) Pitfalls in Human Research (Oxford, Pergamon Press).

Elementary Applications of Probability Theory H. C. TUCKWELL, 1988 London, Chapman & Hall xiii+ 218 pp., ?10.95 ISBN 0 412 30490 2

Elementary Applications of Probability Theory is to be recommended as a well-written and extremely readable introduction to a wide range of applications of probability theory. The book is intended for those who already have some knowledge of probability and statistics and as such provides the minimum of introductory material on probability and random variables. It is nevertheless elementary in its presentation, clearly defining all terms used and proving all results stated with an appealing emphasis on graphical illustrations and worked examples as a means of clarifying the theoretical material. As such it is readily accessible to undergraduates and all those with only minimal statistical knowledge.

The content of the book is broad in scope. After an initial brief chapter on basic probability, the book moves swiftly on to consider geometric probability and in particular the well-known Buffon's needle problem and the distance between points dropped randomly in a circle. Chapter 3 considers the capture-recapture problem as an application of the hypergeometric distribution and includes an interesting diversion into the use of maximum likelihood and the formation of approximate confidence intervals for point and interval estimation of the population size. The second part of Chapter 3 concentrates on the Poisson distribution and Poisson processes in one and two dimensions, including the consideration of ecological patterns in the spatial distribution of plants and animals. The fourth chapter is concerned with reliability theory and refers in particular to failure rates of components. The chapter progresses to the setting up of complex systems and the derivation of system reliability functions for parallel and series systems.

In view of the widespread use of simulation in all areas of statistical research, discussion of the method of simulating random variables, as given in Chapter 5, has to be an important and welcome addition to an undergraduate textbook. The chapter covers methods for simulating uniform random variables, the use of invertible distribution functions as a means of simulating random variables from other families and the polar method of generating normal random variables.

The sixth chapter contains theoretical material to be used in subsequent chapters. It includes characteristic functions, the central limit theorem, convergence in probability and the weak law of large numbers. Despite the complexity of the subjects it seeks to convey, the chapter maintains the clarity and simplicity present throughout the rest of the text. The remaining four chapters introduce random processes including simple random walks, Markov chains, branching processes and birth and death processes. Examples are drawn widely from population genetics, demography and population growth.

The book throughout is problem-centred. Theoretical material is introduced only when an application demands it. As a result it has been possible for the author to cover a tremendous amount of material and provide insights into an array of very varied applications. As such it provides only a small taste for each subject and this limitation is recognised in the text by the inclusion of further reading lists. Each chapter moreover includes a plentiful supply of exercises, varying from the straightforward to the more advanced.

The authors intention to produce a textbook suitable for a second course in probability is in my opinion admirably fulfilled by this volume. However, for me, its strength would be in its use as a companion to more conventional probability textbooks, as a source of examples and real-life applications to make even the most weighty theoretical course in probability digestible to the student. Moreover its plentiful supply of exercises offer a rich resource for those of us who lack either the time or imagination to create our own.

JACKY WILSON University of Bristol, UK

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