Allan Gut

An Intermediate Course in Probability (eBook, PDF)

• Format: PDF

Produktbeschreibung

The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability the ory before entering into more advanced courses (in probability and/or statistics). The presentation is fairly thorough and detailed with many solved examples. Several examples are solved with different methods in order to illustrate their different levels of sophistication, their pros, and their cons. The motivation for this style of exposition is that experi ence has proved that the hard part in courses of this kind usually in the application of the results and methods; to know how, when, and where to apply what; and then, technically, to solve a given problem once one knows how to proceed. Exercises are spread out along the way, and every chapter ends with a large selection of problems. Chapters I through VI focus on some central areas of what might be called pure probability theory: multivariate random variables, condi tioning, transforms, order variables, the multivariate normal distribution, and convergence. A final chapter is devoted to the Poisson process be cause of its fundamental role in the theory of stochastic processes, but also because it provides an excellent application of the results and meth ods acquired earlier in the book. As an extra bonus, several facts about this process, which are frequently more or less taken for granted, are thereby properly verified.

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Produktdetails

• Verlag: Springer New York
• Seitenzahl: 278
• Erscheinungstermin: 17. April 2013
• Englisch
• ISBN-13: 9781475724318
• Artikelnr.: 44184195

Inhaltsangabe

Multivariate Random Variables.- Conditioning.- Transforms.- Order Statistics.- The Multivariate Normal Distribution.- Convergence.- An Outlook on Further Topics.- The Poisson Process.

Rezensionen

From the reviews of the second edition:

"This is an excellent introductory book on random variables, with a wealth of examples and exercises. ... The material is very well organized ... . The text is remarkably well written, mathematically and aesthetically; layout and fonts make it a pleasant reading, and the examples are often enlightening. I think it will be a valuable support for students and instructors and it should definitely find a place in every good library." (Fabio Mainardi, The Mathematical Association of America, October, 2009)

"...A worthwhile addition to the textbook pool, one that will guide the student safely through to a point of competence and ability to embark on a more advanced study..." (International Statistical Review, 2010, 78, 1, 134-159)

"The book addresses a unique niche mathematically inclined students previously exposed to an introductory course in probability ... . The writing style is lucid and easy to follow. ... book is clearly directed toward mathematicians and the highly mathematically inclined scientist or engineer who might be induced to study the mathematics of probability or mathematical statistics. For those who find the classical mathematical pedagogy motivating or those requiring a comprehensive readable reference work on the mathematics of probability theory the book can be highly recommended." (Thomas D. Sandry, Technometrics, Vol. 53 (1), February, 2011)

"This book ... is intended as an introductory graduate level textbook in probability for statistics majors. ... This book provides an elaborate description and a collection of results in probability theory. ... The level of this book is suitable for a graduate course. Overall all concepts are well discussed with full mathematical rigor. ... has a good collection of most of the results related to probability theory, the price is very reasonable, and I will recommend this book to university mathematics and statisticslibraries." (Sounak Chakraborty, Journal of the American Statistical Association, Vol. 106 (495), September, 2011)