Probability Theory (Communications and Signal Processing Collection)

Probability Theory is a classic topic in the educational market, which evolved from the amalgamation of different areas of Mathematics.

Probability Theory is fundamental to most areas of knowledge, including the Engineering, Mathematics, Physics, Sciences, Economics, Social Sciences, Finance, and Health Sciences. It is part of the syllabus for most courses in Mathematics and Engineering.

For Electrical Engineering courses it is a pre-requisite to most disciplines, including stochastic processes, communication systems, source coding, modulation systems, transmission techniques, channel coding, signal analysis, information theory, stochastic control, estimation and digital signal processing.

This book is designed for a course in modern probability.

The book begins with the historical evolution of probability. It then introduces the basic concepts of set theory, measure theory, the axiomatic theory of probability, random variables and multidimensional random variables, functions of random variables, convergence theorems, laws of large numbers, fundamental inequalities.

Appendices include Fourier transforms in one and two dimensions, and important formulas and inequalities. Many examples, illustrations and graphics help the reader understand the theory.

Probability Theory is perfect for graduate students who may not have taken basic courses in these specific topics, and provides a quick and concise way to obtain the knowledge they need to succeed in advanced courses.

Marcelo Sampaio de Alencar received his bachelor's degree in electrical engineering, from the Federal University of Pernambuco, his master's degree from the Federal University of Paraiba, Brazil, and his PhD from the University of Waterloo, Canada. Marcelo S. Alencar has 36 years of experience, as a professional engineer. He is chair professor at the Department of Electrical Engineering, Federal University of Campina Grande. He is founder and president of the Institute for Advanced Studies in Communications. He published over 350 engineering and scientific papers and nineteen books.

Raphael Tavares de Alencar obtained his bachelor's and master's degrees in electrical engineering from the Federal University of Campina Grande. He was involved in an international exchange program at the École Nationale Supérieure des Systémes Avancés et Réseaux, Valence, France. He worked as a consulting engineer, and his main activities included development, manufacture, installation and testing of security systems to protect machine operators. He also worked at the Laboratoire de Conception et d'Intégration des Systèmes, to develop and manufacture chipless RFID readers. He was a researcher in a project funded by National Research Network, developed at the Institute for Advanced Studies in Communications.