620-201 Probability

Students may only gain credit for one of 620-201, [01]620-203, 620-370, 431-325.

One of [00]620-111, 620-120 (MUPHAS Mathematics), 620-121, 620-140, 620-141 and one of 620-131, [01]620-112, 620-122, 620-142, [05]620-192, [05]620-194, 620-211, 620-113, 620-123, 620-143, [05]620-193.

This subject offers a thorough grounding in the fundamental concepts and tools of mathematical probability, probability modelling and simulation. Basic concepts covered include random experiments and sample spaces, probability axioms and theorems, discrete and continuous random variables/distributions (including measures of location, spread and shape), expectations, and generating functions.

The probability distributions and models discussed in the course arise frequently in real world applications. These include the Binomial, Geometric, Negative Binomial, Hypergeometric, Poisson, Exponential, Gamma, Uniform and Normal distributions and three fundamental probability models - Poisson processes, Markov chains and Branching processes. Two dimensional (bivariate) distributions are also introduced (particularly the Bivariate Normal), leading naturally to an examination of notions of independence and dependence (covariance and correlation). Methods for deriving the distribution of various transformations of random variables are also explored.

Analysing models by 'conditioning' on the occurrence of a given event leads to the powerful tools and formulae of conditional probabilities, conditional distributions and conditional expectations.

In computer labs students will learn to use software for both standard probability calculations and simulations of more complex probability models.

Up to 50 pages of written assignments during semester (20%) and a 3-hour end-of-semester written examination (80%).