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**Probability for applications.**
*(English)*
Zbl 0693.60001

Springer Texts in Statistics. New York etc.: Springer-Verlag. xix, 679 p. DM 118.00 (1990).

This book on probability applications contains various chapters on this area. It seems impossible to teach it even in one year, which explains the existence of a commented guide for use in teaching, according to the time available. The applications are essentially motivations, somewhat detailed, than a real situation of applications, even thinking of the chapters on counting processes, Poisson processes and Markov sequences. For instance, the use of Poisson processes in telephone traffic and queuing is not pointed out where applications could be derived from. Also, the book lacks a chapter on extreme values, an important field now, the references made to them being light and short. At the same proposed level we do not find the Berry-Esseen result.

Essentially, the book, using as background linear algebra and calculus, gives the basic probability, some random variables (with a very introductory description of reliability), expectation (the theory of integrals), with some results on moments and regression, and some basic results on conditional expectations with the “applications” already mentioned.

As a book on probability theory it contains more theoretical material than the usual average books, with various motivations, but being far from an advanced probability text. The applications part is weak. There are a few minor misprints. It seems that this book will be more useful for the teacher as an auxiliary text for proofs, motivations etc. than a textbook for students on probability and applications, after the basic introductory average level course on probability.

Essentially, the book, using as background linear algebra and calculus, gives the basic probability, some random variables (with a very introductory description of reliability), expectation (the theory of integrals), with some results on moments and regression, and some basic results on conditional expectations with the “applications” already mentioned.

As a book on probability theory it contains more theoretical material than the usual average books, with various motivations, but being far from an advanced probability text. The applications part is weak. There are a few minor misprints. It seems that this book will be more useful for the teacher as an auxiliary text for proofs, motivations etc. than a textbook for students on probability and applications, after the basic introductory average level course on probability.

Reviewer: J.Tiago de Oliveira