• Offered by Research School of Engineering
• ANU College ANU College of Engineering and Computer Science
• Course subject Engineering
• Areas of interest Mathematics, Engineering
• Course convener
• Dr Nan Yang
• Mode of delivery In Person
• Offered in First Semester 2015
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:

On successful completion of the course, students should be able to:

• Explain fundamentals of probability theory, random variables and random processes.
• Understand the mathematical concepts related to probability theory and random processes.
• Understand the characterization of random processes and their properties.
• Formulate and solve the engineering problems involving random processes.
• Analyze the given probabilistic model of the problem.
• Make precise statements about random processes.
• Use computational techniques to generate simulation results.

## 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

Assignments 18%

Computer Labs (CLabs) 6%

Term Project 6%

Midterm Exam 20%

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). Weekly lectures and laboratories

## Requisite and Incompatibility

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

## Prescribed Texts

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
2015 \$3096
International fee paying students
Year Fee
2015 \$4146
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
2724 16 Feb 2015 06 Mar 2015 31 Mar 2015 29 May 2015 In Person N/A