Designed for graduate-level courses, this text has defined the course of study in probability theory, highly regarded for its strong mathematical orientation and comprehensive coverage. The book classifies topics in probability, random variables, and stochastic processes very logically, carefully incorporating a wide range of illustrations and applications. This edition contains a substantial revision of Parts II & III with greater emphasis on realistic methods of spectral estimation and analysis, and many new problems, examples and applications.

Part I: Probability and random variables -- The meaning of probability -- The axioms of probability -- Repeated trials -- The concept of a random variable -- Functions on one random variable -- Two random variables -- Moments and conditional distributions -- Sequences of random variables -- Statistics -- Part II: Stochastic processes -- General concepts -- Basic applications -- Spectral representation -- Spectral estimation -- Mean square estimation -- Entropy -- Selected topics.