MTH2225 · Mathematics of uncertainty (Advanced)

Overview

This unit provides an introduction to probability - mathematical treatment. Topics include: probability axioms, conditional probabilities and the law of total probability, discrete and continuous random variables, univariate and multivariate distributions, independence and conditioning, conditional distributions and conditional expectations, moment generating functions, simulation, the law of large numbers and the central limit theorem.

Areas of study: Applied mathematics Financial and insurance mathematics Mathematical statistics Mathematics Pure mathematics

Offerings

Assessment

The Handbook lists an examination for this unit.

Assessment details may change. Please refer to the assessment information in Moodle closer to the start of the teaching period.

Requisites

The Handbook lists no prerequisite, corequisite or prohibition for this unit.

Learning outcomes

1. Model and interpret uncertainty using probability spaces, independence, conditional probability, and a range of discrete and continuous distributions, including multivariate contexts;
2. Analyse and compute expectations, variances, moments, and distributions, applying key results such as the Law of Large Numbers, Central Limit Theorem, and moment generating functions;
3. Apply simulation techniques and random number generation to approximate probabilities, expectations, and the behaviour of random processes;
4. Communicate probabilistic reasoning effectively and apply probability models to formulate and solve real-world problems in science, engineering, finance, and related disciplines;
5. Develop rigorous proofs of fundamental results in probability using advanced tools such as conditioning, generating functions, convergence concepts, and limit theorems.

Workload

• Three 1-hour seminars; • One 2-hour applied class (in weeks 2-12); • One 1-hour workshop and • 6 hours of independent study per week.

Student experience, not official rules. Nothing here changes what the Handbook says.