Introduction to Probability, Statistics, and Random Processes

Introduction to Probability, Statistics, and Random Processes by Hossein Pishro-Nik offers a clear and rigorous overview of essential topics in probability and statistics, alongside the fundamental principles of random processes. This comprehensive work is tailored for students and practitioners in fields such as engineering, the sciences, and finance. The book begins with basic concepts including random experiments, probability axioms, and conditional probability, reinforced with practical counting methods. It then advances to cover single and multiple random variables - in discrete, continuous, and mixed forms - along with detailed discussions of moment-generating functions, characteristic functions, random vectors, and associated inequalities. Further sections introduce both classical and Bayesian statistical approaches, and provide insightful coverage of various random processes, including the processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motion. The text also integrates simulation techniques using MATLAB, R, and Python to bridge theory with practical application through a rich collection of solved exercises. With a structure designed to minimize interdependencies between topics, this book allows for maximum flexibility, making it an indispensable resource for instructors and a clear, accessible guide for students seeking to master the subject.