This course starts with the topic of Markov chain. It includes the Chapman-Kolmogorov equations, random walk, classification of states, limiting probabilities, and time reversibility. The second topic in the course is stopping time and martingales. This includes Wald’s equation, the concept of martingale, and the martingale stopping theorem. The third topic is exponential distribution, Poisson distribution, and Poisson process. This includes the unique memoryless property of the exponential distribution, combining and splitting a Poisson random variable, method of randomization, various equivalent definitions for a Poisson process, and M/M/1 queue. Throughout the course, many examples of applications are related to communications and computers.

Advisory: Students are expected to have basic background in probability.