Probability and Random Models (ELEN90054)

Graduate courseworkPoints: 12.5On Campus (Parkville)

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Overview

Availability
Semester 1
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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: 4 March 2025

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
Semester 2 (On Campus - Parkville)
Semester 1 (On Campus - Parkville)
Summer Term (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 1 (On Campus - Parkville)
Semester 2 (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: 4 March 2025

Assessment

DescriptionTimingPercentage

One written examination

  • 3 hours
Hurdle requirement: Students must score above a hurdle requirement on the total of the written exam and the two progress tests. This hurdle requirement will be set by the Board of Examiners and be no higher than 50%.		During the examination period50%

Continuous assessment of submitted project work and quizzes, not exceeding 30 pages over the semester

  • 40-45 hours (of work required)
Throughout the teaching period30%

1-hour Progress Test 1 10% (week 5-6) and 1-hour Progress Test 2 10% (week 10-11)

  • 2 hours
Throughout the semester20%

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: 4 March 2025

Dates & times

  • Semester 1
    Mode of deliveryOn Campus (Parkville)
    Contact hours36 hours of lectures, up to 24 hours of tutorials/workshops
    Total time commitment200 hours
    Teaching period 3 March 2025 to 1 June 2025
    Last self-enrol date14 March 2025
    Census date31 March 2025
    Last date to withdraw without fail 9 May 2025
    Assessment period ends27 June 2025

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: 4 March 2025

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:

    TypeName
    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.

    Please note Single Subject Studies via Community Access Program is not available to student visa holders or applicants

    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: 4 March 2025