620-201 Probability

Students may only gain credit for one of [99]620-001, [99]620-005, 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, [99]620-200, 620-211, 620-113, 620-123, 620-143.

This subject introduces the fundamental concepts of probability, probability modelling and simulation. Students should develop the ability to use simple probability models and carry out standard probability calculations. They should learn to apply standard distributions to calculate probabilities and to use simulations to approximate probabilities. This subject demonstrates the breadth of application of probability, the principles of probability modelling and the application of computer software in probability calculations.

Simple probability models topics include Bernoulli trials, Poisson processes, sampling models, and the use of conditional probability. Random variables topics include descriptions of their probability distributions, probability mass function, probability density function, cumulative distribution function and quantiles, and expectation. Standard distributions topics include hypergeometric, binomial, geometric, negative binomial, Poisson, normal, exponential and gamma distributions and their applications; and mean, variance and other moments. Transformations topics include distribution of g(X), and approximations to the mean and variance of g(X). Random variables topics include descriptions of their probability distributions; expectation of g(X,Y); bivariate normal distribution; covariance and correlation; independence of random variables; distribution of g(X,Y), where X and Y are independent; and conditional distributions, conditional means and variances and their uses. Probability generating functions topics include applications; random sums; and branching processes. Other topics include Markov chains; simulation of random variables and processes; moment generating functions; and the law of large numbers and the central limit theorem.

This subject contributes to developing students' generic skills as well. These include the ability to adopt new ideas, from participation in the lecture program, to use simple probability models and carry out standard calculations, and to develop creative ways of solving unfamiliar problems, especially through practice classes.

A 3-hour end-of-semester written examination. Up to 50 pages of assignments may be assessed.