Introduction to Probability Theory and Stochastic Processes - 9781118382790

The range of probabilities is the interval [0,1]. Chiasson, a professor of electrical and computer engineering, uses the fact that all values in this interval are real numbers and that any real number can be represented as a binary expansion in base 1/2 and thus mapped onto an infinite number of fair coin tosses. It is from this that the author proceeds to define all of probability theory in this graduate level textbook. Unsurprisingly, the first chapter concerns the mathematics of coin tossing. Subsequent chapters cover countable and uncountable sample spaces, continuous random variables, functions of one and two random variables, conditional probabilities for countable sample spaces and continuous random variables, Bernoulli, geometric and Poisson processes, Brownian motion and white noise, and convergence of random variables. The text concludes with chapters on statistics and the Kalman filter. At the end is a list of suggested further reading and a table of common distributions. There is also a set of computer programs written in Matlab that can be downloaded from the publisher's website. This is a very thorough treatment of the topic that rests on a solid theoretical foundation. Annotation ©2013 Book News, Inc., Portland, OR (booknews.com)