MXB101 Probability and Stochastic Modelling 1
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: | MXB101 |
|---|---|
| Equivalent(s): | MAB210 |
| Credit points: | 12 |
| Timetable | Details in HiQ, if available |
| Availabilities |
|
| CSP student contribution | $555 |
| Domestic tuition unit fee | $3,324 |
| International unit fee | $4,296 |
Unit Outline: Semester 1 2024, Gardens Point, Internal
| Unit code: | MXB101 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB210 |
| Coordinator: | David Warne | david.warne@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 statistics, operations research 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, central limit theorem, and introduction to Markov chains. This unit is appropriate for those requiring an introduction to, or a refresher in, probability. The concepts in this unit will be extended in MXB241.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of the basic concepts of introductory probability and stochastic modelling.
- Critically select and apply stochastic models and justify decisions.
- Build and use fundamental stochastic models for real world problems.
- Communicate in mathematical formats to specialist audiences.
Content
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, evaluation of model assumptions using goodness of fit tests, introduction to discrete bivariate distributions. Introduction to stochastic processes. Simple Markov chains, Poisson processes.
Learning Approaches
This unit combines weekly pre-recorded lectures and workshop activities with guided formative online quizzes to reinforce and self-assess your learning. Theory and concepts will be presented and discussed in lectures, utilising examples from a range of real-world applications and purely mathematical scenarios. 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 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
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments, student perusal of marked assessment pieces 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 learning 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
These consist 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. The individual components of the exercises and problems will be marked with feedback to help with your understanding.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
Assesses the skills, problem-solving and operational knowledge you have developed over the whole semester.
The examination will require attendance 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 local testing centre information.
Academic Integrity
Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.
Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.
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.
Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.
Resources
There is no set text 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.
Resource Materials
Reference book(s)
Bertsekas, D.P. and J.N. Tsitsiklis: Introduction to Probability. 2nd edition. Athena Scientific 2008.
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:
Ross, Sheldon M.: A first course in probability. 8th edition, Pearson, 2008.
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
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
Relates to: Problem Solving Task, Examination (invigilated)
Relates to: Problem Solving Task
3: Professional and Personal Attributes
Relates to: Problem Solving Task, Examination (invigilated)
Unit Outline: Semester 1 2024, Online
| Unit code: | MXB101 |
|---|---|
| Credit points: | 12 |
| Equivalent: | MAB210 |
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 statistics, operations research 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, central limit theorem, and introduction to Markov chains. This unit is appropriate for those requiring an introduction to, or a refresher in, probability. The concepts in this unit will be extended in MXB241.
Learning Outcomes
On successful completion of this unit you will be able to:
- Demonstrate knowledge of the basic concepts of introductory probability and stochastic modelling.
- Critically select and apply stochastic models and justify decisions.
- Build and use fundamental stochastic models for real world problems.
- Communicate in mathematical formats to specialist audiences.
Content
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, evaluation of model assumptions using goodness of fit tests, introduction to discrete bivariate distributions. Introduction to stochastic processes. Simple Markov chains, Poisson processes.
Learning Approaches
This unit combines weekly pre-recorded lectures and workshop activities with guided formative online quizzes to reinforce and self-assess your learning. Theory and concepts will be presented and discussed in lectures, utilising examples from a range of real-world applications and purely mathematical scenarios. 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 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
Feedback on Learning and Assessment
Formative feedback will be provided for the in-semester assessment items by way of written comments, student perusal of marked assessment pieces 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 learning 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
These consist 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. The individual components of the exercises and problems will be marked with feedback to help with your understanding.
This assignment is eligible for the 48-hour late submission period and assignment extensions.
Assessment: Examination (invigilated)
Assesses the skills, problem-solving and operational knowledge you have developed over the whole semester.
The examination will require attendance 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 local testing centre information.
Academic Integrity
Students are expected to engage in learning and assessment at QUT with honesty, transparency and fairness. Maintaining academic integrity means upholding these principles and demonstrating valuable professional capabilities based on ethical foundations.
Failure to maintain academic integrity can take many forms. It includes cheating in examinations, plagiarism, self-plagiarism, collusion, and submitting an assessment item completed by another person (e.g. contract cheating). It can also include providing your assessment to another entity, such as to a person or website.
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.
Further details of QUT’s approach to academic integrity are outlined in the Academic integrity policy and the Student Code of Conduct. Breaching QUT’s Academic integrity policy is regarded as student misconduct and can lead to the imposition of penalties ranging from a grade reduction to exclusion from QUT.
Resources
There is no set text 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.
Resource Materials
Reference book(s)
Bertsekas, D.P. and J.N. Tsitsiklis: Introduction to Probability. 2nd edition. Athena Scientific 2008.
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:
Ross, Sheldon M.: A first course in probability. 8th edition, Pearson, 2008.
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
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
Relates to: Problem Solving Task, Examination (invigilated)
Relates to: Problem Solving Task
3: Professional and Personal Attributes
Relates to: Problem Solving Task, Examination (invigilated)