Lars Holst

Sannolikhetsteori och statistikteori har vidsträckta tillämpningar inom olika forskningsområden och olika delar av samhällslivet. Bland annat naturvetare och tekniker har god nytta av kunskaper om dessa teorier och deras användning.Denna bok, som är en omarbetning av en tidigare bok av Gunnar Blom, behandlar de grundläggande delarna av sannolikhetsteorinoch statistikteorin. De många lösta exemplen i texten underlättar läsningen. Övningsproblem med svar avslutar flertalet kapitel.Boken är avsedd för kurser av olika slag men är också lämplig för självstudier.Från och med sjunde upplagan ges denna bok åter ut som hårdband. Denna upplaga innehåller dock inga förändringar av innehållet jämfört med femte och sjätte upplagan.

We, the authors of this book, are three ardent devotees of chance, or some­ what more precisely, of discrete probability. When we were collecting the material, we felt that one special pleasure of the field lay in its evocation of an earlier age: many of our 'probabilistic forefathers' were dexterous solvers of discrete problems. We hope that this pleasure will be transmitted to the readers. The first problem-book of a similar kind as ours is perhaps Mosteller's well-known Fifty Challenging Problems in Probability (1965). Possibly, our book is the second. The book contains 125 problems and snapshots from the world of prob­ ability. A 'problem' generally leads to a question with a definite answer. A 'snapshot' is either a picture or a bird's-eye view of some probabilistic field. The selection is, of course, highly subjective, and we have not even tried to cover all parts of the subject systematically. Limit theorems appear only seldom, for otherwise the book would have become unduly large. We want to state emphatically that we have not written a textbook in probability, but rather a book for browsing through when occupying an easy-chair. Therefore, ideas and results are often put forth without a machinery of formulas and derivations; the conscientious readers, who want to penetrate the whole clockwork, will soon have to move to their desks and utilize appropriate tools.

The Poisson `law of small numbers' is a central principle in modern theories of reliability, insurance, and the statistics of extremes. It also has ramifications in apparently unrelated areas, such as the description of algebraic and combinatorial structures, and the distribution of prime numbers. The law of small numbers is only an approximation. In 1975, a new technique was introduced, the Stein-Chen method, which makes it possible to estimate the accuracy of the approximation in a wide range of situations. This book provides an introduction to the method, and a varied selection of examples of its application, emphasizing the flexibility of the technique when combined with a judicious choice of coupling. It also contains more advanced material, in particular on compound Poisson and Poisson process approximation, where the reader is brought to the boundaries of current knowledge.