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Probability and Random Models (ELEN90054)
Graduate courseworkPoints: 12.5On Campus (Parkville)
About this subject
- Overview
- Eligibility and requirements
- Assessment
- Dates and times
- Further information
- Timetable (login required)(opens in new window)
Contact information
Semester 1
Jonathan Manton jmanton@unimelb.edu.au
Overview
Availability | Semester 1 |
---|---|
Fees | Look up fees |
AIMS
This subject provides an introduction to probability theory, random variables, random vectors, decision tests, and stochastic processes. Uncertainty is inevitable in real engineering systems, and the laws of probability offer a powerful way to evaluate uncertainty, to predict and to make decisions according to well-defined, quantitative principles. The material covered is important in fields such as communications, data networks, signal processing and electronics. This subject is a core requirement in the Master of Engineering (Electrical, Mechanical and Mechatronics).
INDICATIVE CONTENT
Topics include:
- Foundations – combinatorial analysis, axioms of probability, independence, conditional probability, Bayes’ rule;
- Random variables (rv’s)– definition; cumulative distribution, probability mass and probability density functions; expectation and variance; functions of an rv; important distributions and their properties and uses;
- Multiple random variables – joint cumulative distribution, probability mass and probability density functions; independent rv’s; correlation and covariance; conditional distributions and expectation; functions of several rv’s; jointly Gaussian rv’s; random vectors;
- Sums, inequalities and limit theorems – sums of rv’s, moment generating function; Markov and Chebychev inequalities; weak and strong laws of large numbers; the Central Limit Theorem;
- Decision testing - maximum likelihood, maximum a posterior, minimum cost and Neyman-Pearson rules; basic minimum mean-square error estimation;
- Stochastic processes – mean and autocorrelation functions, strict and wide-sense stationarity; ergodicity; important processes and their properties and uses;
- Introduction to Markov chains.
This material is complemented by exposure to examples from electrical engineering and software tools (e.g. MATLAB) for computation and simulations.
Intended learning outcomes
INTENDED LEARNING OUTCOMES (ILOs)
Having completed this subject it is expected that the student be able to:
- Demonstrate an understanding of combinatorics, the axioms of probability, independence, random variables, conditioning and Bayes’ rule
- Demonstrate an understanding of important distributions, stochastic processes and decision tests, and their significance
- Formulate random models of signals and systems encountered in engineering
- Calculate and interpret probabilities, probability densities, means, variances and covariances, from given information
- Use the law of large numbers, the central limit theorem, and inequalities to find approximations and bounds
- Simulate random models using software tools
Generic skills
On completion of this subject, students will have developed the following skills:
- Ability to apply knowledge of basic science and engineering fundamentals;
- In-depth technical competence in at least one engineering discipline;
- Ability to undertake problem identification, formulation and solution;
- Ability to utilise a systems approach to design and operational performance;
- Capacity for independent critical thought, rational inquiry and self-directed learning;
- Ability to communicate effectively, with the engineering team and with the community at large.
Last updated: 31 January 2024
Eligibility and requirements
Prerequisites
Graduate Students:
Admission into or selection of one of the following:
- MC-ELECENG Master of Electrical Engineering
- MC-BIOMENG Master of Biomedical Engineering
- MC-MTRNENG Master of Mechatronics Engineering
- Electrical specialisation (formal) in the MC-ENG Master of Engineering
- Biomedical specialisation (formal) in the MC-ENG Master of Engineering
- Mechatronics specialisation (formal) in the MC-ENG Master of Engineering
- Electrical with Business specialisation (formal) in the MC-ENG Master of Engineering
Undergraduate Students:
One of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10006 | Calculus 2 |
Summer Term (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
MAST10009 | Accelerated Mathematics 2 | Semester 2 (On Campus - Parkville) |
12.5 |
MAST10021 | Calculus 2: Advanced | Semester 2 (On Campus - Parkville) |
12.5 |
AND
One of
Code | Name | Teaching period | Credit Points |
---|---|---|---|
MAST10007 | Linear Algebra |
Summer Term (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
Semester 2 (On Campus - Parkville)
|
12.5 |
MAST10008 | Accelerated Mathematics 1 | Semester 1 (On Campus - Parkville) |
12.5 |
MAST10022 | Linear Algebra: Advanced | Semester 1 (On Campus - Parkville) |
12.5 |
Corequisites
None
Non-allowed subjects
ELEN30002 Stochastic Signals and Systems
Recommended background knowledge
Knowledge in one of the following subjects is recommended:
Code | Name | Teaching period | Credit Points |
---|---|---|---|
ELEN30012 | Signals and Systems |
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
|
12.5 |
BMEN30006 | Circuits and Systems | Semester 1 (On Campus - Parkville) |
12.5 |
Inherent requirements (core participation requirements)
The University of Melbourne is committed to providing students with reasonable adjustments to assessment and participation under the Disability Standards for Education (2005), and the Assessment and Results Policy (MPF1326). Students are expected to meet the core participation requirements for their course. These can be viewed under Entry and Participation Requirements for the course outlines in the Handbook.
Further details on how to seek academic adjustments can be found on the Student Equity and Disability Support website: http://services.unimelb.edu.au/student-equity/home
Last updated: 31 January 2024
Assessment
Description | Timing | Percentage |
---|---|---|
One written examination
| During the examination period | 50% |
Continuous assessment of submitted project work and quizzes, not exceeding 30 pages over the semester
| Throughout the teaching period | 30% |
1-hour Progress Test 1 10% (week 5-6) and 1-hour Progress Test 2 10% (week 10-11)
| Throughout the semester | 20% |
Additional details
Intended Learning Outcomes (ILOs) 1 to 5 are assessed in the final written examination, the mid-semester test, quizzes and submitted reports for several computer-based workshops.
ILO 6 is assessed through the workshop reports.
Last updated: 31 January 2024
Dates & times
- Semester 1
Coordinator Jonathan Manton Mode of delivery On Campus (Parkville) Contact hours 36 hours of lectures, up to 24 hours of tutorials/workshops Total time commitment 200 hours Teaching period 26 February 2024 to 26 May 2024 Last self-enrol date 8 March 2024 Census date 3 April 2024 Last date to withdraw without fail 3 May 2024 Assessment period ends 21 June 2024 Semester 1 contact information
Jonathan Manton jmanton@unimelb.edu.au
Time commitment details
200 hours
What do these dates mean
Visit this webpage to find out about these key dates, including how they impact on:
- Your tuition fees, academic transcript and statements.
- And for Commonwealth Supported students, your:
- Student Learning Entitlement. This applies to all students enrolled in a Commonwealth Supported Place (CSP).
Subjects withdrawn after the census date (including up to the ‘last day to withdraw without fail’) count toward the Student Learning Entitlement.
Last updated: 31 January 2024
Further information
- Texts
Prescribed texts
Probability and Stochastic Processes, Yates and Goodman, Wiley
Recommended texts and other resources
TBA
- Subject notes
LEARNING AND TEACHING METHODS
The subject is delivered through lectures, tutorials and workshop classes.
INDICATIVE KEY LEARNING RESOURCES
Students are provided with lecture slides, worked problem sets and reference text lists.
CAREERS / INDUSTRY LINKS
Exposure to simulation tools and teamwork through the six workshops.
- Related Handbook entries
This subject contributes to the following:
Type Name Specialisation (formal) Electrical with Business Specialisation (formal) Electrical Specialisation (formal) Mechatronics - Available through the Community Access Program
About the Community Access Program (CAP)
This subject is available through the Community Access Program (also called Single Subject Studies) which allows you to enrol in single subjects offered by the University of Melbourne, without the commitment required to complete a whole degree.
Entry requirements including prerequisites may apply. Please refer to the CAP applications page for further information.
Additional information for this subject
Subject coordinator approval required
- Available to Study Abroad and/or Study Exchange Students
This subject is available to students studying at the University from eligible overseas institutions on exchange and study abroad. Students are required to satisfy any listed requirements, such as pre- and co-requisites, for enrolment in the subject.
Last updated: 31 January 2024