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.
• 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.
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