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.