3 Hours/Week, 3 Credits

Modern probability theory: probability of a set function, Borel field and extension of probability measure, probability measure notion of random variables, probability space, distribution functions, expectation and moments. Inversion theorem. Convergence of random variables: characteristic functions with properties, probability generating functions with properties, conditions, modes of convergence. Stochastic process: definition, different types of stochastic processes, recurrent events, renewal equation, delayed recurrent events, number of occurrence of a recurrent event. Markov chain: transition matrix, higher transition probabilities, classification of states and chains, ergodic properties, evaluation of pn. Finite Markov chain: general theory of random walk with reflecting barriers, transient states, absorbing probabilities, application of recurrence time, gamblerís ruin problem. Homogeneous Markov process: Poisson process, simple birth process, simple death process, simple birth and death process, general birth process, effect of immigration, non-homogeneous birth death process. Queueing theory.