The purpose of this book is to provide the reader with a solid background andunderstanding of the basic results and methods in probability theory beforeentering... » 

The purpose of this book is to provide the reader with a solid background andunderstanding of the basic results and methods in probability theory beforeentering into more advanced courses. The first six chapters focus on somecentral areas of what might be called pure probability theory multivariaterandom variables conditioning transforms order variables the multivariatenormal distribution convergence. A final chapter is devoted to the Poissonprocess as a means both to introduce stochastic processes and to apply many ofthe techniques introduced earlier in the text. Students are assumed to havetaken a first course in probability though no knowledge of measure theory isassumed. Throughout the presentation is thorough and includes many examplesthat are discussed in detail. Thus students considering more advanced researchin probability theory will benefit from this wideranging survey of the subjectthat provides them with a foretaste of the subjects many treasures. Thepresent second edition offers updated content one hundred additional problemsfor solution and a new chapter that provides an outlook into further areas andtopics such as stable distributions and domains of attraction extreme valuetheory and records and martingales. The main idea is that this chapter mayserve as an appetizer to the more advanced theory. TOCIntroduction.Multivariate Random Variables. Conditioning. Transforms. Order statistics.The multivariate normal distribution. Convergence. An outlook into furthertopics. The Poisson Process. «