MXN501 Stochastic Modelling
To view more information for this unit, select Unit Outline from the list below. Please note the teaching period for which the Unit Outline is relevant.
| Unit code: | MXN501 |
|---|---|
| Prerequisite(s): | Completion of 144 credit points in EU50 Master of Teaching (Secondary) OR (192cps in SV03 or SV04 or IV04 or IV05 or BV06 or BV07 or EV08 or EV07) OR (admission into IV53 or IV57 or IV54 or IV59 or IV52 or IV56 or IV51 or IV58 or IV60) OR (admission into IN20 or IN27 or IN31) |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
| CSP student contribution | $578 |
| Domestic tuition unit fee | $3,612 |
| International unit fee | $4,836 |
Unit Outline: Semester 2 2025, Gardens Point, Internal
| Unit code: | MXN501 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | Completion of 144 credit points in EU50 Master of Teaching (Secondary) OR (192cps in SV03 or SV04 or IV04 or IV05 or BV06 or BV07 or EV08 or EV07) OR (admission into IV53 or IV57 or IV54 or IV59 or IV52 or IV56 or IV51 or IV58 or IV60) OR (admission into IN20 or IN27 or IN31) |
| Coordinator: | Mahdi Abolghasemi | mahdi.abolghasemi@qut.edu.au |
Overview
This unit introduces probability and shows you how to apply its concepts to solve practical problems. The unit will lay the foundations for further studies in probability, statistics and other areas of mathematics and help you to develop your problem-solving and modelling skills. The topics covered include: basic probability rules, conditional probability and independence, discrete and continuous random variables, bivariate distributions, Markov chains and Poisson processes. This unit is appropriate for those requiring an introduction to, or a refresher in, probability. The concepts in this unit will be extended in MXN601.
Learning Outcomes
On successful completion of this unit you will be able to:
- Appropriately apply the basic concepts of introductory stochastic and statistical modelling.
- Draw on knowledge of probability, random variables and distributions to identify and solve problems.
- Competently and critically build and use stochastic and statistical models for real world problems.
- Work in a group to solve problems and express a coherent argument.
Content
The topics in this unit develop knowledge of and skills in applying: the fundamental concepts of statistical modelling including: probability theory and axioms, and the probability distributions that are the foundations of statistical and probabilistic modelling across disciplines. Consequently, this unit develops problem-solving skills relevant to all quantitative areas involving uncertainty and data analytics.
The unit does not assume any prior knowledge of probability and distributions (though such knowledge is likely to be of advantage) as this is developed in the first part of the unit. However, the unit takes for granted the full range of algebraic skills taught up to high school year 10 and builds on a general mathematical understanding and some of the skills (such as integration) that are typically acquired in Senior Mathematics B (or equivalent).
The mathematical content of the unit includes, but is not limited to, all or almost all of the following topics:
- Foundations of probabilistic modelling
Probability rules and language; Kolmogorov axioms; independence and conditional probability; law of total probability and Bayes' rule; discrete and continuous random variables and distributions (such as Bernouilli, binomial, geometric, Poisson, uniform and exponential distributions); expected value and variance - Introduction to stochastic processes
Simple Markov chains; Poisson processes.
The emphasis throughout is on applications in both familiar and new contexts, and on skills for describing and setting up problems, and identifying methods and tools to solve them. This implies that the focus of this course is not on developing calculation skills, but most of all on developing a conceptual understanding of stochastic and statistical thinking that allows for approaching practical problems by building stochastic and statistical models in a competent, creative and critical way.
Simple strategies for working in groups to solve relevant problems will also be explored to prepare you for group assessment work. The standards for presentation and communication of mathematical and statistical information will be discussed and demonstrated by example.
Learning Approaches
This unit involves 2 hours of lectures each week where theory and concepts will be presented and discussed, and where you will be exposed to the processes required to solve problems using the methods of this unit. There will be the opportunity for participation and interaction. There will also be 2 hour of workshop activities each week.
Whenever possible, you will be introduced to new topics by exploring and understanding your existing knowledge which will then be formalised and developed. The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios. The emphasis will be on learning by doing, learning in groups and as individuals, written and oral communication, and developing skills and attitudes to promote life-long learning. The standards of the discipline as well as appropriate approaches to the communication of mathematical and statistical information will be conveyed via the examples presented in lectures and workshops.
In workshops, a combination of discussion, working through small and larger real world problems and expressing solutions individually and in groups, will promote your creativity in problem-solving, critical assessment skills, and intellectual debate.
The most valuable learning approach is for you to do all the problem solving tasks. These will enable you to synthesise concepts, techniques and applications, and assist you in developing all the key knowledge that later parts of the unit, other units at a later stage of your studies and the final exam of this unit will be based on.
Full solutions to all problem-solving tasks will be made available on Canvas progressively. All materials required for the semester, will be available on Canvas.
Feedback on Learning and Assessment
Full solutions will be provided in a timely manner for all formative and summative assessment in problem-solving throughout the semester. Feedback on individual work will also be provided during workshop classes. Ongoing guidance will be provided with individual development of skills, knowledge and confidence in tackling problems, in working individually and in groups and in communication.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
All assessment in this unit is skills-based and operational assessment. The focus is on problem-solving skills using operational knowledge and understanding of key concepts, techniques and procedures.
The assessment package is carefully designed to help you manage and optimise your learning throughout the semester, allowing for different individual situations and capabilities. The assessment package will help you develop your understanding and skills throughout the semester, aiming for achievement of the synergies and synthesis of the unit by the end of semester.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Workbook
These consist of exercises and problems strategically timed to optimise your learning. They cover the core operational knowledge and skills of the unit and provide you with an excellent way of learning through applying techniques to real problems within context. The individual components of the exercises and problems will be marked with feedback to help with understanding and given to you within two weeks of submission of each. Further assessment details will be posted on Canvas.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
This is a written exam assessing the skills, problem-solving and operational knowledge you have developed over the whole semester.
Academic Integrity
Academic integrity is a commitment to undertaking academic work and assessment in a manner that is ethical, fair, honest, respectful and accountable.
The Academic Integrity Policy sets out the range of conduct that can be a failure to maintain the standards of academic integrity. This includes, cheating in exams, plagiarism, self-plagiarism, collusion and contract cheating. It also includes providing fraudulent or altered documentation in support of an academic concession application, for example an assignment extension or a deferred exam.
You are encouraged to make use of QUT’s learning support services, resources and tools to assure the academic integrity of your assessment. This includes the use of text matching software that may be available to assist with self-assessing your academic integrity as part of the assessment submission process.
Breaching QUT’s Academic Integrity Policy or engaging in conduct that may defeat or compromise the purpose of assessment can lead to a finding of student misconduct (Code of Conduct – Student) and result in the imposition of penalties under the Management of Student Misconduct Policy, ranging from a grade reduction to exclusion from QUT.
Resources
There are no set texts for this unit.
There are many reference texts for this unit, many of which can be located in the library. There are also many online resources such as lecture notes and some e-books that can be found online. Example reference texts are listed below.
1. Bertsekas, D.P. and J.N. Tsitsiklis: Introduction to Probability. 2nd edition. Athena Scientific 2008.
2. Grinstead, C.M. and J.L. Snell: Introduction to Probability. 2nd revised edition, American Mathematical Society, 1997. A free copy can be downloaded under GNU FDL:
3. Ross, Sheldon M.: A first course in probability. 8th edition, Pearson, 2008.
4. Schaeffer, R.L. and L.J. Young: Introduction to Probability and its Applications. 3rd edition, Brooks/Cole (or earlier editions authored by Schaeffer only).
Risk Assessment Statement
There are no out of the ordinary risks associated with this unit, as all classes will be held in ordinary lecture theatres. Emergency exits and assembly areas will be pointed out in the first few lectures. You are referred to the University policy on health and safety.
http://www.mopp.qut.edu.au/A/A_09_01.jsp