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.

Research-Led Teaching

During the course, we make connections to state-of-the-art electronic engineering technologies (such as those used in cellular networks, robotic systems, and computing) and research activities where appropriate. Practice of using programming languages, e.g. Matlab, to model, design and analyse electronic engineering systems gives hand-on experiences of simulation-aided research and development.

Field Trips

N/A

Additional Course Costs

N/A

Recommended Resources

Primary textbook

• J. A. Gubner, Probability and Random Processes for Electrical and Computer Engineers, Cambridge University Press, 2006.

Suggested textbooks

• S. L. Miller and D. Childers, Probability and Random Processes: With Applications to Signal Processing and Communications.
• 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.

Library Reserves

• Probability and Random Processes for Electrical and Computer Engineers
• Probability, Random Variables, and Stochastic Processes
• Probability and Random Processes

Website

• Programs and Courses (Course description)
• Wattle (Course Wattle page)
• It is students' responsibility to regularly check the webpage (at least twice a Week) for course information and announcements. 

Staff Feedback

Students will be given feedback in the following forms in this course:

1. Direct verbal feedback to the course convener and tutors.

2. Written feedback presented in the course Wattle page to address the collected comments and suggestions.

3. Verbal or written feedback on marked assignments and project reports.

4. Indirect feedback through class representative(s) and the Associate Director (Education).

Student Feedback

ANU is committed to the demonstration of educational excellence and regularly seeks feedback from students. Students are encouraged to offer feedback directly to their Course Convener or through their College and Course representatives (if applicable). Feedback can also be provided to Course Conveners and teachers via the Student Experience of Learning & Teaching (SELT) feedback program. SELT surveys are confidential and also provide the Colleges and ANU Executive with opportunities to recognise excellent teaching, and opportunities for improvement.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	Introduction to the Course, basic concepts in probability theory, functions and sets, probability models, axioms of probability, independence, combinatorics and binomial probabilities
2	Discrete random variables (RVs): Probability mass function (PMF), multiple RVs, statistics of RVs, useful inequalities.	Assignment 1 released.
3	Discrete RVs: Correlation and covariance, conditional PMF, substitution law, conditional expectation. Continuous RVs: Probability density function (PDF) and important continuous RVs. Tutorial 1.
4	Continuous RVs: Expectation of a continuous RV, moment generating function (MGF), characteristic function (CF), cumulative distribution function (CDF), CDF of mixed random variables, CDF and PDF of a function of RVs, and central limit theorem.	Assignment 1 due. Assignment 2 released.
5	Continuous RVs: Bivariate random variables, joint PDF and CDF, marginal PDF and CDF, conditional PDF and CDF, and bivariate Gaussian. Tutorial 2.	Project topics released.
6	Stochastic processes: Introduction, classification, characterisation, and stationary process.	Assignment 2 due.
7	Stochastic processes: Ergodicity, power spectral density (PSD), noise classification and characterisation, and WSS processes through linear time-invariant (LTI) systems.
8	Stochastic processes: Matched filter design, Wiener filter design, causal Wiener filter design, and validity of correlation functions and PSD functions. Tutorial 3.	Assignment 3 released.
9	Stochastic processes: Poisson process and renewal process. Markov chain: Discrete Markov chain and examples, state transition, and stationary distribution.	CLab 1.
10	Estimation: Non-parametric spectral estimation, parametric spectral estimation, and properties of a good estimator.	Assignment 3 due.
11	Estimation: Maximum likelihood estimation, Bayesian estimation, and minimum mean-squared error estimation. Tutorial 4.	CLab 2.
12	Project group presentation	Project group presentation.

Tutorial Registration

Students are automatically included into the tutorial session by the course convener in the MyTimetable system.

Assessment Summary

Assessment task	Value	Learning Outcomes
Assignments	15 %	1, 2, 3, 4, 5, 6, 7, 8
Computer Labs (CLabs)	6 %	1, 2, 3, 4, 5, 6
Term Project	9 %	1, 2, 3, 4, 7, 8
Mid-semester Exam	20 %	1, 2, 3, 4, 5, 6
Final Exam	50 %	1, 2, 3, 4, 5, 6

* If the Due Date and Return of Assessment date are blank, see the Assessment Tab for specific Assessment Task details

Policies

ANU has educational policies, procedures and guidelines , which are designed to ensure that staff and students are aware of the University’s academic standards, and implement them. Students are expected to have read the Academic Integrity Rule before the commencement of their course. Other key policies and guidelines include:

• Academic Integrity Policy and Procedure
• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Guideline and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure
• Code of practice for teaching and learning

Assessment Requirements

The ANU is using 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. For additional information regarding Turnitin please visit the Academic Skills website. In rare cases where online submission using Turnitin software is not technically possible; or where not using Turnitin software has been justified by the Course Convener and approved by the Associate Dean (Education) on the basis of the teaching model being employed; students shall submit assessment online via ‘Wattle’ outside of Turnitin, or failing that in hard copy, or through a combination of submission methods as approved by the Associate Dean (Education). The submission method is detailed below.

Moderation of Assessment

Marks that are allocated during Semester are to be considered provisional until formalised by the College examiners meeting at the end of each Semester. If appropriate, some moderation of marks might be applied prior to final results being released.

Assessment Task 1

Assignments

1. There are 3 assignments, each worth 5% of the total mark. Assignments are based on relevant materials in textbooks and lecture slides, while some offline research may need to be conducted.

2. Assignments carry significant weightage in overall assessment. Assignments are required to be submitted according to the due dates and time shown below, where the date and time are based on Australian Eastern Standard Time (Canberra):

* Assignment 1: Due Date: 19 March 2023; Cut-off Date: 24 March 2023.

* Assignment 2: Due Date: 2 April 2023; Cut-off Date: 7 April 2023.

* Assignment 3: Due Date: 14 May 2023; Cut-off Date: 19 May 2023.

3. Submit an electronic copy of your solution as a single PDF file in Wattle. Please ensure that you use the assignment coversheet provided in Wattle as the front page. Please include your name and student number, tick the correct assignment number, and write corresponding due date on the coversheet.

4. Submission by the due date does not incur any penalty. Late submission after the due date and prior to the cut-off date is allowed, but a penalty of five per cent of the possible marks available for assignments per working day or part thereof is applied. No submission is allowed after the cut-off date.

5. Students are required to solve assignment assignments independently, which will greatly help students to perform satisfactorily in the exams.

Assessment Task 2

Computer Labs (CLabs)

1. There are two CLabs, one running in Week 9 and the other one running in Week 11. The labs focus on simulation techniques and application of random processes using Matlab.

2. Students need to attend both CLabs. If two lab sessions are available, students can choose either lab session 1 on Tuesday or lab session 2 on Wednesday. The lab report is not required. Each student’s performance will be assessed by the lab demonstrator based on the satisfactory completion of tasks as outlined in the lab manual. The marking will be undertaken during the lab.

3. Students need to read the CLab manual and relevant lectures BEFORE starting the CLab, and complete the lab procedure described in the CLab manual during the CLab.

4. All students are required to complete two CLabs.

Assessment Task 3

Term Project

1. The objective of the project (worth 9% of the total mark) is to apply the materials covered in the course to real-life problems or engineering systems. The project helps students on their retention of course materials and significantly enhances the depth of students’ understanding. The project is expected to consume roughly 4-5 weeks of moderately concentrated effort.

2. Students should form groups of 2 to carry out the term project. It is the responsibility of group members to ensure that all members participate in a fair and equitable manner. The two members of a group are expected to receive the similar mark. Any grouping difficulties should be resolved early in the semester.

3. Each group is allowed to choose either Method A or Method B to complete the term project. The details of the two methods are given as follows:

* Method A: Students design and develop a project topic in the field of engineering and/or computing, based on their background, expertise and past experiences. This self-designed topic needs to be relevant to the knowledge of probability and stochastic processes, and approved by the course convener. It is noted that the proposed project topic should not be used in other courses. Then students are required to identify and study the key problems in this topic which can be advanced or solved by the knowledge of probability and stochastic processes.

* Method B: Students select a project topic from the list proposed by the course convener. Then students are required to read and understand the research papers provided by the course convener. Despite so, students are encouraged to choose their preferred research paper(s) if the provided research papers do not meet their requirements.

4. After the project topic is confirmed, by either Method A or Method B, the main task for students is to obtain a comprehensive understanding of the background and recent development of the topic, as well as an in-depth understanding on the technical aspect of the key problems or research papers.

  * Useful questions for the project topic include:

   a) Why do people (such as researchers, scientists, engineers and industrial professionals) investigate and advance this topic? What are the impacts of this topic on the human society?

   b) What are the current progress and future trend of this topic?

   c) In general, how is the knowledge of probability and stochastic processing applied in this topic?

  * Useful questions for the key problems in Method A include:

   d) What is the problem? Why is the problem important?

   e) What are the challenges to solve the problem?

   f) How did people solve the problem by using the knowledge of probability and stochastic processes?

   g) What are the main results when people solve the problem?

   h) What are the limitations of current approaches to solving the problem? If you are asked to address such limitations, e.g. by using another set of knowledge, what will you do?

 * Useful questions for the research papers in Method B include:

   i) Which problem does the paper study?

   j) What are the innovation and novelty of the paper?

   k) How did authors solve the problem by using the knowledge of probability and stochastic processes?

   l) What are the main results and findings of the paper?

   m) How can the results of this paper be extended to address new scenarios/requirements or how can the limitations of the results be addressed by using another set of knowledge?

5. The duration of the presentation for the term project will be regulated in the document titled Presentation Assessment Criteria.

6. Each presentation will be followed by questions from the assessors (including the lecturer and tutors).

7. The presentations will be delivered in Week 12.

8. The PowerPoint/PDF version of the presentation slides need to be sent to the course convener after the presentation.

Assessment Task 4

Mid-semester Exam

Mid-semester exam worth 20% of the total mark, and is planned to be scheduled in Week 7.

Assessment Task 5

Final Exam

Final exam worth 50% of the total mark, and is planned to be scheduled during the final examination period.

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. The University’s students are an integral part of that community. The academic integrity principle commits all students to engage in academic work in ways that are consistent with, and actively support, academic integrity, and to uphold this commitment by behaving honestly, responsibly and ethically, and with respect and fairness, in scholarly practice.

The University expects all staff and students to be familiar with the academic integrity principle, the Academic Integrity Rule 2021, the Policy: Student Academic Integrity and Procedure: Student Academic Integrity, and to uphold high standards of academic integrity to ensure the quality and value of our qualifications.

The Academic Integrity Rule 2021 is a legal document that the University uses to promote academic integrity, and manage breaches of the academic integrity principle. The Policy and Procedure support the Rule by outlining overarching principles, responsibilities and processes. The Academic Integrity Rule 2021 commences on 1 December 2021 and applies to courses commencing on or after that date, as well as to research conduct occurring on or after that date. Prior to this, the Academic Misconduct Rule 2015 applies.

 

The University commits to assisting all students to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. All coursework students must complete the online Academic Integrity Module (Epigeum), and Higher Degree Research (HDR) students are required to complete research integrity training. The Academic Integrity website provides information about services available to assist students with their assignments, examinations and other learning activities, as well as understanding and upholding academic integrity.

Online Submission

Students should submit assignments via Wattle. This course does not use Turnitin for assignment submission since it cannot properly handle scanned handwritten solutions and equations.

Hardcopy Submission

N/A

Late Submission

Assignments: Submission by the due date does not incur any penalty. Late submission after the due date and prior to the cut-off date is allowed, but a penalty of five per cent of the possible marks available for assignments per working day or part thereof is applied. No submission is allowed after the cut-off date.

Referencing Requirements

The Academic Skills website has information to assist you with your writing and assessments. The website includes information about Academic Integrity including referencing requirements for different disciplines. There is also information on Plagiarism and different ways to use source material.

Returning Assignments

Marked assignments returned within two weeks of the cut-off date.

Extensions and Penalties

Extensions and late submission of assessment pieces are covered by the Student Assessment (Coursework) Policy and Procedure. Extensions may be granted for assessment pieces that are not examinations or take-home examinations. If you need an extension, you must request an extension in writing on or before the due date. If you have documented and appropriate medical evidence that demonstrates you were not able to request an extension on or before the due date, you may be able to request it after the due date.

Privacy Notice

The ANU has made a number of third party, online, databases available for students to use. Use of each online database is conditional on student end users first agreeing to the database licensor’s terms of service and/or privacy policy. Students should read these carefully. In some cases student end users will be required to register an account with the database licensor and submit personal information, including their: first name; last name; ANU email address; and other information.
In cases where student end users are asked to submit ‘content’ to a database, such as an assignment or short answers, the database licensor may only use the student’s ‘content’ in accordance with the terms of service – including any (copyright) licence the student grants to the database licensor. Any personal information or content a student submits may be stored by the licensor, potentially offshore, and will be used to process the database service in accordance with the licensors terms of service and/or privacy policy.
If any student chooses not to agree to the database licensor’s terms of service or privacy policy, the student will not be able to access and use the database. In these circumstances students should contact their lecturer to enquire about alternative arrangements that are available.

Distribution of grades policy

Academic Quality Assurance Committee monitors the performance of students, including attrition, further study and employment rates and grade distribution, and College reports on quality assurance processes for assessment activities, including alignment with national and international disciplinary and interdisciplinary standards, as well as qualification type learning outcomes.

Since first semester 1994, ANU uses a grading scale for all courses. This grading scale is used by all academic areas of the University.

Support for students

The University offers students support through several different services. You may contact the services listed below directly or seek advice from your Course Convener, Student Administrators, or your College and Course representatives (if applicable).

• ANU Health, safety & wellbeing for medical services, counselling, mental health and spiritual support
• ANU Access and inclusion for students with a disability or ongoing or chronic illness
• ANU Dean of Students for confidential, impartial advice and help to resolve problems between students and the academic or administrative areas of the University
• ANU Academic Skills and Learning Centre supports you make your own decisions about how you learn and manage your workload.
• ANU Counselling Centre promotes, supports and enhances mental health and wellbeing within the University student community.
• ANUSA supports and represents undergraduate and ANU College students
• PARSA supports and represents postgraduate and research students