ABSTRACT
This chapter discusses aspects of discrete probability that are relevant to mathematics, computer science, engineering, and other disciplines. It includes random variables, important discrete probability distributions, random walks, Markov models, queues, simulation, and the probabilistic method. The chapter also presents various applications to genetics, telephone network performance, reliability, average-case algorithm analysis, and combinatorics. Sequences of independent events are often encountered when an experiment is repeated. Independent events correspond, intuitively, to events that do not affect the outcome of one another. The treatment of dependent events requires conditional probabilities. Many discrete probability computations are much less straightforward than may at first be imagined because of difficulties arising from the finiteness of computer arithmetic systems. Good algorithm design can usually avoid such problems.
