Probability and Random Models

This subject provides an introduction to probability theory, random variables, random vectors, decision tests, and stochastic processes. Uncertainty is inevitable in real engineering systems, and the laws of probability offer a powerful way to evaluate uncertainty, to predict and to make decisions according to well-defined, quantitative principles. The material covered is important in fields such as communications, data networks, signal processing and electronics. This subject is a core requirement in the Master of Engineering (Electrical, Mechanical and Mechatronics).

• 1Demonstrate an understanding of combinatorics, the axioms of probability, independence, random variables, conditioning and Bayes’ rule
• 2Demonstrate an understanding of important distributions, stochastic processes and decision tests, and their significance
• 3Formulate random models of signals and systems encountered in engineering
• 4Calculate and interpret probabilities, probability densities, means, variances and covariances, from given information
• 5Use the law of large numbers, the central limit theorem, and inequalities to find approximations and bounds
• 6Simulate random models using software tools