An Intermediate Course in Probability

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.

This book covers the basic results and methods in probability theory. This new edition offers updated content, 100 additional problems for solution, and a new chapter glimpsing further topics such as stable distributions, domains of attraction and martingales.

Includes supplementary material: sn.pub/extras

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