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Dice, Data and Decisions

This is a timely appearance of a textbook that brings the applications of probability theory to the attention of both undergraduate and postgraduate students of probability and particularly of operational research. The following should be pointed out to someone seeing the title of this book for the first time. (1) The treatment of the material is mathematical and at an intermediate level. A thorough knowledge of basic probability, calculus and elementary differential equations is assumed. (2) Not all of the many important techniques of applied probability are discussed. For example, the treatment of Markov chains is omitted. Beginning with the Poisson process the author proceeds to birth and death processes, queueing theory, renewal theory, reliability and inventory control. Each section usually introduces the concepts and ideas at an intuitive and descriptive level before producing the mathematical formulation. A combination of methods such as differential equations, generating functions and Laplace transforms are then applied to give the standard results. The average student (whose needs, as the preface of this book indicates, have been uppermost in the author's mind) will be pleased by the detailed, almost step-by-step, derivation of the important results. Each section provides a collection of theoretical problems and the reader should attempt to solve them as they are indispensable to the understanding of the subject matter. Copious hints for their solution are presented at the end of the chapters. To conclude with, there are appendices on probability generating functions, Laplace transforms and computing the mean of a distribution. What is lacking is an additional appendix dealing with the theorem of total probability and its use in the context of this book. The average student would certainly appreciate this as it would clarify even further some of the derivations and proofs. Although the treatment is mathematical, the emphasis is not on abstraction and generality. This allows the author to present the reader with an exceptionally clear exposition of the basics of reliability and inventory control, topics which are usually relegated to the advanced approach of postgraduate textbooks. This is an excellent text for academic purposes. However, the student will have to look elsewhere in order to ascertain how these techniques of probability are actually used by the practitioner in 'real-life' situations.