Introduction to probability : multivariate models and applications / N. Balakrishnan, Markos V. Koutras, and Konstantinos G. Politis.

Includes bibliographical references and index.

Two-dimensional discrete random variables and distributions -- Two-dimensional continuous random variables and distributions -- Independence and multivariate distributions -- Transformations of variables -- Covariance and correlation -- Important multivariate distributions -- Generating functions -- Limit theorems.

"Probability theory is the branch of mathematics concerned with analysis of random phenomena. The central objects of probability theory are random variables, stochastic processes, and events: mathematical abstractions of non-deterministic events or measured quantities that may either be single occurrences or evolve over time in an apparently random fashion. Although an individual coin toss or the roll of a die is a random event, if repeated many times the sequence of random events exhibits certain statistical patterns, which can be studied and predicted. Two representative mathematical results describing such patterns are the law of large numbers and the central limit theorem. As a mathematical foundation for statistics, probability theory is essential to many human activities that involve quantitative analysis of large sets of data. Methods of probability theory also apply to descriptions of complex systems given only partial knowledge of their state, as in statistical mechanics. The multivariate normal distribution or multivariate Gaussian distribition, is a generalization of the one-dimensional (univariate) normal distribution to higher dimensions. A random vector is said to be multivariate normally distributed if every linear combination of its components has a univariate normal distribution. The multivariate normal distribution is often used to describe, at least approximately, any set of (possibly) correlated real-valued random variables, each of which clusters around a mean value"-- Provided by publisher.