• Offered by School of Engineering
• ANU College ANU College of Engineering Computing & Cybernetics
• Course subject Engineering
• Areas of interest Mathematics, Engineering
• Work Integrated Learning Projects
• Academic career PGRD
• Course convener
• AsPr Nan Yang
• Mode of delivery In Person
• Offered in First Semester 2024
• STEM Course
Probability and Stochastic Processes in Engineering (ENGN8538)

The objective of ENGN8538 is to provide the fundamentals and advanced concepts of probability theory and random process to support graduate coursework and research in electrical, electronic and computer engineering. The required mathematical foundations will be studied at a fairly rigorous level and the applications of the probability theory and random processes to engineering problems will be emphasised. The simulation techniques will also be studied and MATLAB will be used as a software tool for bridging the probability theory and engineering applications.

Topics include:

• Overview of elementary probability;

• Discrete and continuous random variables and their statistical properties;

• Important random variables and their applications;

• Functions of random variables;

• Statistical properties of multiple random variables;

• Random processes: Classification and characterisation;

• Properties of random processes: Stationarity, correlation function, power spectral density, spectral analysis;

• Special processes: such as Gaussian and Poisson;

• Overview of Markov process and applications;

• Estimation theory, MMSE estimation, performance comparison of estimators;

• Overview of detection theory;

• Simulation techniques: generation of random variable/process in MATLAB;

• Examples of applications from signal processing (e.g., Wiener filter), digital communications (e.g., analysis and simulation of coded digital communication system) and mechatronic systems (e.g. estimation in simultaneous localisation and mapping).

## Learning Outcomes

Upon successful completion, students will have the knowledge and skills to:

1. Apply the specialised knowledge in probability theory and random processes to solve practical engineering problems.
2. Gain advanced and integrated understanding of the fundamentals of and interrelationship between discrete and continuous random variables and between deterministic and stochastic processes.
3. Apply the fundamentals of probability theory and random processes to practical engineering problems, and identify and interpret the key parameters that underlie the random nature of the problems.
4. Use the top-down approach to translate engineering system requirements into practical design problems.
5. Create mathematical models for practical design problems and determine theoretical solutions to the created models.
6. Analyse the performance in terms of probabilities and distributions achieved by the determined solutions.
7. Apply research skills to develop a thorough understanding of emerging engineering research problems beyond the scope of the course materials and critically analyse the recent research outcomes.
8. Professionally interpret and disseminate the design and results of engineering research problems to the audiences with different levels of background knowledge.

## Work Integrated Learning

### Projects

This course provides the fundamentals and advanced concepts of probability theory and random process to support graduate coursework and research in electrical, electronic and computer engineering.

This course provides you with the opportunity to deeply engage with the course content, drive your leaning, build skills and confidence,

and perform the learned tasks more effectively.

## Other Information

Professional Skills Mapping:

## Indicative Assessment

1. Assignments (15) [LO 1,2,3,4,5,6,7,8]
2. Computer Labs (6) [LO 1,2,3,4,5,6]
3. Term Project (9) [LO 1,2,3,4,7,8]
4. Midterm Exam (20) [LO 1,2,3,4,5,6]
5. Final Exam (50) [LO 1,2,3,4,5,6]

The ANU uses Turnitin to enhance student citation and referencing techniques, and to assess assignment submissions as a component of the University's approach to managing Academic Integrity. While the use of Turnitin is not mandatory, the ANU highly recommends Turnitin is used by both teaching staff and students. For additional information regarding Turnitin please visit the ANU Online website.

Standard workload (approx. 10 hours a week). 2 lectures (1 x 2-hour lecture and 1 x 1-hour lecture) per week, up to 1 x 1-hour tutorial per week, up to 1 x 3-hour computer laboratories per week, approximately 6 hours independent study per week.

Not applicable

## Requisite and Incompatibility

To enrol in this course you must be studying Master of Engineering.

## Prescribed Texts

The prescribed text for this course is:
• J. A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press, 2006.

• S. L. Miller and D. Childers, Probability and Random Processes: With Applications to Signal Processing and Communications. (Online reserve: http://www.sciencedirect.com/science/book/9780121726515 )
• A. Papoulis and S.U. Pillai, Probability, Random Variables, and Stochastic Processes.
• H. Stark and J. Woods, Probability, Random Processes, and Estimation Theory for Engineers.
• G. R. Grimmett and D. R. Stirzaker, Probability and Random processes.

## Assumed Knowledge

• ENGN2228 Signal Processing or equivalent (Suggested)
• Assume understanding of basic fundamentals of probability theory and linear algebra

## Fees

Tuition fees are for the academic year indicated at the top of the page.

Commonwealth Support (CSP) Students
If you have been offered a Commonwealth supported place, your fees are set by the Australian Government for each course. At ANU 1 EFTSL is 48 units (normally 8 x 6-unit courses). More information about your student contribution amount for each course at Fees

Student Contribution Band:
2
Unit value:
6 units

If you are a domestic graduate coursework student with a Domestic Tuition Fee (DTF) place or international student you will be required to pay course tuition fees (see below). Course tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Where there is a unit range displayed for this course, not all unit options below may be available.

Units EFTSL
6.00 0.12500

## Course fees

Domestic fee paying students
Year Fee
2024 \$4980
International fee paying students
Year Fee
2024 \$6360
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

ANU utilises MyTimetable to enable students to view the timetable for their enrolled courses, browse, then self-allocate to small teaching activities / tutorials so they can better plan their time. Find out more on the Timetable webpage.

The list of offerings for future years is indicative only.
Class summaries, if available, can be accessed by clicking on the View link for the relevant class number.

### First Semester

Class number Class start date Last day to enrol Census date Class end date Mode Of Delivery Class Summary
2325 19 Feb 2024 26 Feb 2024 05 Apr 2024 24 May 2024 In Person View

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