Also, more complicated counting problems will be discussed. The emphasis of the course will be on techniques for analyzing and solving problems. The importance of probability theory is difficult to overstate. The appropriate mathematical model for the study of a large number of observational phenomena is a probabilistic one rather than a deterministic one. In addition, the entire subject of statistical inference is based on probabilistic considerations.
Statistical techniques are among the most important tools of scientists and engineers.
In order to use these techniques intelligently a thorough understanding of probabilistic concepts is required. In any situations, the second question may not only be the more pertinent one, but in fact, the only meaningful one to ask. Throughout the course, problems and applications will be emphasized. Estimation, decision theory, testing hypothesis, correlation, linear models, and design. General notion of stochastic processes, finite and infinite Markov chains, discrete and continuous Markov processes, stationary processes, random walk problems, birth and death processes, waiting line and serving problems, Brownian motion.