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.