MXB241 Stochastic Processes
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: | MXB241 |
|---|---|
| Prerequisite(s): | MXB107 and MXB105 |
| Equivalent(s): | MAB314 |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
Unit Outline: Semester 2 2027, Gardens Point, Internal
| Unit code: | MXB241 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | MXB107 and MXB105 |
| Equivalent: | MAB314 |
| Coordinator: | Chris Drovandi | c.drovandi@qut.edu.au |
Overview
It is important to develop skills and knowledge in both statistics and mathematics. Building on the methodology and skills developed in previous studies in probability and stochastic modelling, this unit provides you with formal statistical tools such as stochastic process models and statistical methods for theoretical and applied development. These methods are useful in a wide range of areas, from communication systems and networks to traffic to law to biology to financial analysis, and link with other modern areas of mathematics. This unit will provide opportunities to learn how to build statistical models of real world processes, acknowledging the assumptions inherent in selected models. The skills developed in this unit will be integral in the understanding of material throughout your studies in statistics and mathematical modelling.
Learning Outcomes
On successful completion of this unit you will be able to:
- Apply advanced concepts, principles and methods of probability and stochastic modelling for analysing processes and data.
- Interpret non-mathematical information to identify variables and use mathematical tools to enable investigation and solution of a given problem.
- Select and justify advanced stochastic models for solving real world problems.
- Communicate statistical conclusions clearly and concisely in written form to a specialist audience.
Content
Developing skills in using mathematical tools to solve statistical problems. Skills and familiarity in describing and setting up problems, and identifying methods and tools to solve them. Skills in communication in problem-solving. Building on earlier studies to develop understanding and ability to work with generating functions, order statistics, sampling distributions, functions of random variables, stochastic models including Markov chains, branching processes, queueing and birth and death processes, and Brownian motion. Developing familiarity and ability to use and interpret parameters and properties of key distributions, and models of stochastic and statistical processes. Developing understanding and skills in using ranks for key statistical procedures in the non-parametric area.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. Learning in this unit includes weekly pre-recorded lectures, interactive lecture, online activities, workshops and a unit communications channel, designed to facilitate communication with your peers and teaching staff outside of scheduled classes.
The pre-recorded lecture content will introduce core concepts and worked examples, and is supported with a live interactive lecture that will allow you to engage with the lecturer. In workshops, you will work with peers and with the teaching team to develop effective methods/approaches for communicating, retrieving, evaluating and presenting information in an ethical way, and you will learn how to work effectively within groups with consideration for cultural differences. The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios.
You can expect to spend 10 - 15 hours per week involved in preparing for and attending all scheduled workshops, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task
This assessment item consists of exercises and problems both in and out of class 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. For each of three submission points you will submit handwritten or typed solutions to around five authentic probability and stochastic problems drawn from real world problems.
The individual components of the exercises and problems will be marked with feedback and returned to you to assist with understanding and future assessment items.
The use of generative artificial intelligence (GenAI) tools is prohibited during this assessment.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
This will consist of a written exam based on and representative of the work covered during the semester.
The use of generative artificial intelligence (GenAI) tools is prohibited during this assessment.
The examination will be at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide testing centre information.
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 is a recommended reference text for this unit. There are also online resources such as lecture notes and some e-books that can be found online.
Resource Materials
Recommended text(s)
Sheldon M Ross, Introduction to Probability Modelling, Academic Press
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
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Problem Solving Task, Examination (invigilated)
2: Engineering Application Ability
Relates to: Problem Solving Task, Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Problem Solving Task, Examination (invigilated)
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.DS01 Bachelor of Data Science
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the data science discipline, with depth of knowledge in at least one area developed through a major.
Relates to: Problem Solving Task, Examination (invigilated) - Use appropriate statistical, computational, modelling, data management, programming and generative artificial intelligence techniques to develop solutions for deriving insights from data.
Relates to: Problem Solving Task, Examination (invigilated) - Demonstrate critical thinking and problem-solving skills, as well as adaptivity in applying learned techniques in new and unfamiliar contexts.
Relates to: Problem Solving Task, Examination (invigilated) - Communicate effectively in a variety of modes, to expert and non-expert audiences, including in a professional context.
Relates to: Problem Solving Task, Examination (invigilated)
MS01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Problem Solving Task, Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Problem Solving Task, Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Problem Solving Task, Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Problem Solving Task, Examination (invigilated)
MV01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Problem Solving Task, Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Problem Solving Task, Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Problem Solving Task, Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Problem Solving Task, Examination (invigilated)
Unit Outline: Semester 2 2027, Online
| Unit code: | MXB241 |
|---|---|
| Credit points: | 12 |
| Pre-requisite: | MXB107 and MXB105 |
| Equivalent: | MAB314 |
Overview
It is important to develop skills and knowledge in both statistics and mathematics. Building on the methodology and skills developed in previous studies in probability and stochastic modelling, this unit provides you with formal statistical tools such as stochastic process models and statistical methods for theoretical and applied development. These methods are useful in a wide range of areas, from communication systems and networks to traffic to law to biology to financial analysis, and link with other modern areas of mathematics. This unit will provide opportunities to learn how to build statistical models of real world processes, acknowledging the assumptions inherent in selected models. The skills developed in this unit will be integral in the understanding of material throughout your studies in statistics and mathematical modelling.
Learning Outcomes
On successful completion of this unit you will be able to:
- Apply advanced concepts, principles and methods of probability and stochastic modelling for analysing processes and data.
- Interpret non-mathematical information to identify variables and use mathematical tools to enable investigation and solution of a given problem.
- Select and justify advanced stochastic models for solving real world problems.
- Communicate statistical conclusions clearly and concisely in written form to a specialist audience.
Content
Developing skills in using mathematical tools to solve statistical problems. Skills and familiarity in describing and setting up problems, and identifying methods and tools to solve them. Skills in communication in problem-solving. Building on earlier studies to develop understanding and ability to work with generating functions, order statistics, sampling distributions, functions of random variables, stochastic models including Markov chains, branching processes, queueing and birth and death processes, and Brownian motion. Developing familiarity and ability to use and interpret parameters and properties of key distributions, and models of stochastic and statistical processes. Developing understanding and skills in using ranks for key statistical procedures in the non-parametric area.
Learning Approaches
This unit is available for you to study in either on-campus or online mode. Learning in this unit includes weekly pre-recorded lectures, interactive lecture, online activities, workshops and a unit communications channel, designed to facilitate communication with your peers and teaching staff outside of scheduled classes.
The pre-recorded lecture content will introduce core concepts and worked examples, and is supported with a live interactive lecture that will allow you to engage with the lecturer. In workshops, you will work with peers and with the teaching team to develop effective methods/approaches for communicating, retrieving, evaluating and presenting information in an ethical way, and you will learn how to work effectively within groups with consideration for cultural differences. The material presented will be context-based utilising examples from a range of real-world applications and purely mathematical scenarios.
You can expect to spend 10 - 15 hours per week involved in preparing for and attending all scheduled workshops, completing assessment tasks, and undertaking your own independent study to consolidate your learning.
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments on the assessment items, student perusal of the marked assessment piece and informal interview as required.
Summative feedback will be provided throughout the semester with progressive posting of results via Canvas.
Assessment
Overview
The assessment items in this unit are designed to determine your level of competency in meeting the unit outcomes while providing you with a range of tasks with varying levels of skill development and difficulty.
Unit Grading Scheme
7- point scale
Assessment Tasks
Assessment: Problem Solving Task
This assessment item consists of exercises and problems both in and out of class 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. For each of three submission points you will submit handwritten or typed solutions to around five authentic probability and stochastic problems drawn from real world problems.
The individual components of the exercises and problems will be marked with feedback and returned to you to assist with understanding and future assessment items.
The use of generative artificial intelligence (GenAI) tools is prohibited during this assessment.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
This will consist of a written exam based on and representative of the work covered during the semester.
The use of generative artificial intelligence (GenAI) tools is prohibited during this assessment.
The examination will be at a local testing centre. For students enrolled as internal or on-campus, the local testing centre will be on QUT campus. For students enrolled as online, QUT Examinations will provide testing centre information.
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 is a recommended reference text for this unit. There are also online resources such as lecture notes and some e-books that can be found online.
Resource Materials
Recommended text(s)
Sheldon M Ross, Introduction to Probability Modelling, Academic Press
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
Standards/Competencies
This unit is designed to support your development of the following standards\competencies.
Engineers Australia Stage 1 Competency Standard for Professional Engineer
1: Knowledge and Skill Base
Relates to: Problem Solving Task, Examination (invigilated)
2: Engineering Application Ability
Relates to: Problem Solving Task, Examination (invigilated)
3: Professional and Personal Attributes
Relates to: Problem Solving Task, Examination (invigilated)
Course Learning Outcomes
This unit is designed to support your development of the following course/study area learning outcomes.DS01 Bachelor of Data Science
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the data science discipline, with depth of knowledge in at least one area developed through a major.
Relates to: Problem Solving Task, Examination (invigilated) - Use appropriate statistical, computational, modelling, data management, programming and generative artificial intelligence techniques to develop solutions for deriving insights from data.
Relates to: Problem Solving Task, Examination (invigilated) - Demonstrate critical thinking and problem-solving skills, as well as adaptivity in applying learned techniques in new and unfamiliar contexts.
Relates to: Problem Solving Task, Examination (invigilated) - Communicate effectively in a variety of modes, to expert and non-expert audiences, including in a professional context.
Relates to: Problem Solving Task, Examination (invigilated)
MS01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Problem Solving Task, Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Problem Solving Task, Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Problem Solving Task, Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Problem Solving Task, Examination (invigilated)
MV01 Bachelor of Mathematics
- Demonstrate a broad and coherent knowledge of the principles, concepts and techniques of the applied mathematical sciences, with depth in at least one area.
Relates to: Problem Solving Task, Examination (invigilated) - Formulate and model problems in mathematical terms and apply appropriate mathematical, statistical and computational techniques to solve practical and abstract problems.
Relates to: Problem Solving Task, Examination (invigilated) - Demonstrate critical thinking and problem solving skills across a range of applied mathematical and statistical contexts, and adaptivity in applying learned techniques in new or unfamiliar contexts.
Relates to: Problem Solving Task, Examination (invigilated) - Present information and articulate arguments and conclusions in a variety of modes, to diverse audiences both expert and non-expert.
Relates to: Problem Solving Task, Examination (invigilated)