• Offered by RS Electrical, Energy and Materials Engineering
• ANU College ANU College of Engineering and Computer Science
• Course subject Engineering
• Areas of interest Mathematics, Engineering
• Course convener
• Prof Pallage Abhayapala
• Mode of delivery In Person
• Offered in First Semester 2019
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;

• Sequence of random variables, random vectors, notions of convergence;

• Random processes: Classification and characterisation;

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

• Special processes: Gaussian, Poisson and Wiener;

• 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 (Wiener filter) and digital communications (simulation of coded digital communication system).

## Learning Outcomes

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

Upon successful completion of the course, students will be able 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.

Professional Skills Mapping
Mapping of Learning Outcomes to Assessment and Professional Competencies

## Other Information

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;

• Sequence of random variables, random vectors, notions of convergence;

• Random processes: Classification and characterisation;

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

• Special processes: Gaussian, Poisson and Wiener;

• 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 (Wiener filter) and digital communications (simulation of coded digital communication system).

## Indicative Assessment

1. Assignments: 18%
2. Computer Labs: 6%
3. Project Presentation: 6%
4. Midterm Exam: 20%
5. Final Exam: 50%

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.

## 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)
• ENGN3226 Digital Communications 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.

If you are a domestic graduate coursework or international student you will be required to pay tuition fees. Tuition fees are indexed annually. Further information for domestic and international students about tuition and other fees can be found at Fees.

Student Contribution Band:
2
Unit value:
6 units

If you are an undergraduate student and 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). You can find your student contribution amount for each course 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
2019 \$4320
International fee paying students
Year Fee
2019 \$5700
Note: Please note that fee information is for current year only.

## Offerings, Dates and Class Summary Links

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
3078 25 Feb 2019 04 Mar 2019 31 Mar 2019 31 May 2019 In Person N/A