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The course presents the fundamentals of probability theory and random processes needed by students in communications and information systems, computer engineering, signal processing, machine learning, bioinformatics, econometrics and mathematical finance. Topics include: History and overview; probability; random variables; functions of random variables; generating functions and transform methods; inequalities, Chernoff's bounds and large deviation theory; convergence and the limit theorems; random processes; spectral representation; Poisson and birth-death processes; Markov chains; random walk, Brownian motion, diffusion and Ito processes.