確率論中級コース（第２版） An Intermediate Course in Probability (Springer Texts in Statistics) （2ND）

Gut, A.

Springer（2009/08発売）

Springer（2009/08発売）

• 製本 Hardcover:ハードカバー版／ページ数 315 p.
• 商品コード 9781441901613

基本説明

A Textbook. Students are assumed to have taken a first course in probability, though no knowledge of measure theory is assumed. Throughout, the presentation
is thorough and includes many examples that are discussed in detail.

Full Description

The purpose of this book is to provide the reader with a solid background and understanding of the basic results and methods in probability theory 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 di erent methods in order to illustrate their di erent levels of sophistication, their pros, and their cons. The motivation for this style of exposition is that experience has proved that the hard part in courses of this kind usually is 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 1 through 6 focus on some central areas of what might be called pure probability theory: multivariate random variables, conditioning, tra- forms, order variables, the multivariate normal distribution, and convergence.

Contents

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