Introduction to Probability, Statistics, and Random Processes

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This book introduces students to probability, statistics, and stochastic processes. It can be used by both students and practitioners in engineering, various sciences, finance, and other related fields. It provides a clear and intuitive approach to these topics while maintaining mathematical accuracy.The book covers: Basic concepts such as random experiments, probability axioms, conditional probability, and counting methodsSingle and multiple random variables (discrete, continuous, and mixed), as well as moment-generating functions, characteristic functions, random vectors, and inequalitiesLimit theorems and convergenceIntroduction to Bayesian and classical statisticsRandom processes including processing of random signals, Poisson processes, discrete-time and continuous-time Markov chains, and Brownian motionSimulation using MATLAB, R, and Python (online chapters)The book contains a large number of solved exercises. The dependency between different sections of this book has been kept to a minimum in order to provide maximum flexibility to instructors and to make the book easy to read for students. Examples of applications-such as engineering, finance, everyday life, etc.-are included to aid in motivating the subject. The digital version of the book, as well as additional materials such as videos, is available at www.probabilitycourse.com.