Introduction to Probability Theory and Stochastic Processes

This book presents an innovative approach to teaching probability theory and stochastic processes. 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 probability distribution on a single probability space. This construction provides the mathematical framework to understand how stochastic processes are viewed and used in applications. It is intended for first year graduate students in Engineering, Mathematics, and Physics.