Theory and applications of discrete probability models. Elementary combinatory analysis, random walks, urn models, occupancy problems, and the binomial and Poisson distributions.
Introduction to Probability Models, Ross, Elsevier/Academic Press, 11th edition
Any realistic model of a real-world phenomenon must take into account the possibility of randomness. That is, more often than not, the quantities we are interested in will not be predictable in advance, but rather, will exhibit an inherent variation that should be taken into account by the model. This is usually accomplished by allowing the model to be probabilistic in nature. Such a model is, naturally enough, referred to as a probability model. This course will be concerned with different probability models of natural phenomena, in particular, we shall focus on the discrete probability models. We shall present some basic probability concepts, random variables, random vectors, expectations, moment generating function, conditioning, Markov chain, Renewal Theory and some applications.
(Hu 2016 )