620-201 Probability

Students may only gain credit for one of 620-201, 620-205, 620-370, 431-325.

Students undertaking Actuarial Studies should take 620-201 instead of 620-205.

One of 620-120 (UMEP Maths for High Achieving Students), 620-121, 620-140, 620-141 and one of 620-131, 620-113, 620-123, 620-143 (grade of H2B or above), [05]620-193 (grade of H2B or above).

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 a number of widely used one-dimensional distributions and fundamental probability models such as Poisson processes and Markov chains. 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. Techniques to obtain the exact and approximate distributions of sums of random variables will be introduced. These methods will be illustrated through some well known normal approximations to discrete distributions and by obtaining the exact and approximate distributions of some commonly used statistics.

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 due during semester (20%); a 3-hour written examination in the examination period (80%).