Multivariate Probability and Stochastic Processes

This book is a comprehensive guide to multivariate probability for students who have an elementary knowledge of probability and are ready to move on to more advanced concepts. Topics covered include: A review of basic probability theory, including core ideas about random variables Bivariate distributions and the general theory of random vectors Relationships between random variables Normal linear model and multivariate sampling distributions Generating functions and convergence Each section is illustrated with numerous examples. Multivariate probability deliberately avoids a measure-theoretic approach in order to make these complex concepts easily accessible to a broad readership. Attention is restricted to discrete and (absolutely) continuous random variables. Although proofs are given of all the main results, this book is primarily intended to provide readers with the tools they require to build appropriate probability models for real-life situations. The usefulness of simulation in this respect is emphasized throughout the book.