Course Contents

This course is an introduction to Markov chains, random walks, martingales, and Galton-Watsom tree etc. The course requires basic knowledge in probability theory and linear algebra including conditional expectation and matrix.

Course Synopsis

• Basic concepts of probability theory and random variables • How to deal with multiple random variables? Conditional probability and conditional expectation, joint distribution and independence, mean square estimation • Anaysis of random process and application to the signal processing in the communication system • Analysis of Queueing Theory and application of the theory to real-world problem

Course Learning Outcomes

Upon successful completion of the course, students will be able to: • Apply the specialised knowledge in probability theory and random processes to solve practical computing problems. • Gain advanced and integrated understanding of the fundamentals of and interrelationship between discrete and continuous random variables and between deterministic and stochastic processes. • Apply the fundamentals of probability theory and random processes to practical computing problems, and identify and interpret the key parameters that underlie the random nature of the problems. • Use the top-down approach to translate computing system requirements into practical design problems. • Create mathematical models for practical design problems and determine theoretical solutions to the created models. • Analyse the performance in terms of probabilities and distributions achieved by the determined solutions. • Apply research skills to develop a thorough understanding of emerging computing research problems beyond the scope of the course materials and critically analyse the recent research outcomes. • Professionally interpret and disseminate the design and results of computing research problems to the audiences with different levels of background knowledge.