Elementary Probability Theory

This is an introductory textbook on probability theory and its applications. Basic concepts such as probability measure, random variable, distribution, and expectation are fully treated without technical complications. Both the discrete and continuous cases are covered, the elements of calculus being used in the latter case. The emphasis is on essential probabilistic reasoning, amply motivated, explained, and illustrated with a large number of carefully selected examples. Special topics include combinatorial problems, urn schemes, Poisson processes, random walks, genetic models, and Markov chains. Problems with solutions are provided at the end of each chapter. Its easy style and full discussion make this a useful text not only for mathematics and statistics majors, but also for students in engineering and physical, biological, and social sciences. This edition adds two new chapters covering applications to mathematical finance. Elements of modern portfolio and option theories are presented in a detailed and rigorous manner. The approach distinguishes this text from other more mathematically advanced treatises or more technical manuals.