Introduction To Probability Theory And Stochastic Processes
Publisher: John Wiley & Sons Inc
Published: April 8, 2013
Place of publication: Hoboken, New Jersey, USA
Language: eng
Format: Hardcover
Number of pages: 984
ISBN-13: 9781118382790
Description: A unique approach to stochastic processes that connects the mathematical formulation of random processes to their use in applications

This book presents an innovative approach to teaching probability theory and stochastic processes based on the binary expansion of the unit interval. Departing from standard pedagogy,it uses the binary expansion of the unit interval to explicitly construct an infinite sequence of independent random variables (of any given distribution) on a single probability space. This construction then provides the framework to understand the mathematical formulation of probability theory for its use in applications.
Notes: This comprehensive textbook provides an introduction to statistical methods for graduate engineers offering thorough coverage of important probability-related topics to aid in product and system design, reliability engineering, quality control, and more. Includes bibliographical references and index.
Table of contents: title: 1 Coin Tossing 1; title: 2 Countable Sample Spaces 61; title: 3 Conditional Probability in Countable Sample Spaces 105; title: 4 Uncountable Sample Spaces 151; title: 5 Continuous Random Variables 213; title: 6 Expectation 245; title: 7 Modeling Random Phenomena 267; title: 8 Functions of One Random Variables and Transforms 321; title: 9 Functions of Two Random Variables 365; title: 10 Two Functions of Two Random Variables 431; title: 11 Conditional Probability for Continuous Random Variables 473; title: 12 Random Vectors 549; title: 13 Bernoulli, Geometric, and Poisson Processes 587; title: 14 Brownian Motions and White Noise 645; title: 15 Stationary Random Processes 703; title: 16 Convergence of Random Variables 777; title: 17 Statistics 839; title: 18 Kalman Filter 905; title: Further Reading 933; title: Table of Common Distributions 935; title: References 941; title: Index 946