620-201 Probability

Credit Points

Coordinator

Prerequisites

One of 620-131, 620-140, 620-160; and one of 620-121 or 620-141 or [98]620-162. First year students with excellent VCE results may be invited by the Head of Department to enter 620-201 directly.

Semester

Contact

Subject Description

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 and to simulate 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: Bernoulli trials, Poisson processes, sampling models, use of conditional probability. Random variables: descriptions of their probability distributions, probability mass function, probability density function, cumulative distribution function and quantiles, expectation. Standard distributions including hypergeometric, binomial, negative binomial, Poisson, normal, exponential and gamma distributions and their applications; mean, variance and other moments. Transformations: distribution of g(X), approximations to the mean and variance of g(X). Bivariate random variables: 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, conditional distributions, conditional means and variances and their uses. Probability generating functions and applications; random sums; branching processes; Markov chains; simulation of random variables and processes. Moment generating functions and the central limit theorem.

Assessment

Up to 3 hours end-of-semester written examination; up to 50 pages of assignments may be assessed.