The objective of this module is to provide the fundamentals and advanced concepts of probability theory and random process to support graduate coursework and research in electrical, electronic and computer engineering. The required mathematical functions are studied at a fairly rigorous level and the applications of the random processes to engineering problems are emphasized. The simulation techniques are be studied and MATLAB is used as a software tool for bridging the probability theory and engineering applications. The course covers probability spaces, random variables, distribution and density functions, expectation, characteristic functions, conditional probability, conditional expectation, sequences of random variables: convergence concepts, laws of large numbers, central limit theorem, large deviation, random vectors and estimation: random vectors, covariance characterization, orthogonality principle and Kalman filtering.