Variability, randomness, risk, and related attributes characterise most measurable phenomena in the real world. Probability and Stochastic Processes are concerned with random phenomena occurring dynamically in time or space, or both. They play a critical role in the theory and methods of a wide range of physical, medical, engineering and social sciences, and many others. A good understanding of probability is essential for the study of Statistics. Probability theory is both mathematically elegant and remarkably practical, and the distinction it makes between deterministic and stochastic modelling is fundamental to real-world applications especially in the areas of insurance risk, genetics and evolutionary biology, climatology, epidemiology, criminology, time series modelling and forecasting, signal processing and detection, and derivatives pricing and financial mathematics.

## Learning Outcomes

Explain the fundamental concepts of probability theory and its position in modern statistical and mathematical sciences and applied contexts

Explain the fundamental concepts of stochastic processes in continuous time and their position in modern statistical and mathematical sciences and applied contexts

Solve complex problems relating to probability theory and stochastic processes in a variety of contexts

Use stochastic calculus in mathematical and financial problems

## Other Information

Students will need to complete all of the following courses in order to be able to complete the 48 units of this major:

- MATH1115 OR MATH1113
- MATH1116
- STAT1003 OR STAT1008 (may be included in the 6 units from completion of further courses from the subject area STAT Statistics)
- STAT2001 OR STAT2013 (may be included in the 6 units from completion of further courses from the subject area STAT Statistics)
- STAT2005 (may be included in the 6 units from completion of further courses from the subject area STAT Statistics)

## Requirements

This major requires the completion of 48 units, which must include:

12 units from completion of the following compulsory courses:

STAT3004 Stochastic Modelling

STAT3006 Advanced Stochastic Processes

12 units from completion of further courses from the subject area STAT Statistics or from the following list:

MATH3015 Mathematics of Finance

MATH3029 Probability Modelling with Applications

Either:

24 units from completion of the following mathematical statistics courses:

MATH2305 Applied Mathematics I

MATH2306 Applied Mathematics II

STAT3013 Statistical Inference

STAT3056 Advanced Mathematical Statistics

Or:

18 units from completion of the following mathematical analysis courses:

MATH2320 Advanced Analysis 1: Metric Spaces and Applications

MATH3320 Advanced Analysis 2: Topology, Lebesgue Integration and Hilbert Spaces

STAT3017 Big Data Statistics

6 units from completion of further courses from the subject area STAT Statistics

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