The course offers an introduction into modern probability theory, including probability spaces, random variables, conditional probability and independence, limit theorems, Markov chains and martingales with an outlook towards advanced stochastic processes. The course will emphasise practical understanding and applications as well as a solid theoretical foundation for the subject.

The course will provide a sound foundation to progress to STAT7006 (Advanced Stochastic Processes), as well as other honours and post-graduate courses emphasizing mathematical finance, stochastic analysis and statistical as well as actuarial sciences.

Learning Outcomes

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

1. Explain in detail the fundamental concepts of probability theory and its position in modern statistical and mathematical sciences and applied contexts;
2. Demonstrate accurate and efficient use of complex probability theory techniques;
3. Demonstrate in depth capacity for mathematical reasoning through analyzing, proving and explaining concepts from probability theory; and
4. Apply complex problem-solving techniques using probabilistic methods in various situations.

Research-Led Teaching

The course provides the up-to-date introduction in the mathematical underpinning of modern probability theory, that is the mathematical theory of uncertainty. Contrived in the 20th century, it is the foundation of any modern research in the area of probability and stochastic processes. Apart from this, it provides useful tools in any area of research dealing with reasoning and uncertainty such as mathematics, statistics, economics, finance, computer science and engineering.

Examination Material or equipment

The final exam will contain material from the entire semester. You will require reliable access to Wattle and a calculator for the duration of the online exams.

Required Resources

A First Look at Rigorous Probability Theory, Second Edition by Jeffrey S. Rosenthal. An electronic copy of the textbook is available from the ANU Library as an ebook

Staff Feedback

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

• Interactions with lecturer and tutor(s) in consultations and live tutorials or recorded lectures.
• Through assessments where the lecturer and tutors will provide specific feedback.

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.

Other Information

Scaling

You final mark for the course will be based on the raw marks allocated for each of your assessment items. However, your final mark may not be the same number as produced by that formulate, as marks may be scaled. Any scaling applied will preserve the rank order of raw marks (i.e. if your raw mark exceeds that of another student, then your scaled mark will exceed or be the same as the scaled mark of that student), and may result in a score that is either higher or lower than the raw mark calculated.

Support for Students

The University offers a number of support services for students. Information on these is available online from http://students.anu.edu.au/studentlife/

Communication

If necessary, the lecturer and tutor(s) for this course will contact students on their official ANU student email address. Information about your enrollment and fees from the Registrar and Student Services' office will also be sent to this email address. Students are expected to check the Wattle site for announcements about this course, e.g. changes to timetables or notifications of cancellations.

Assessment Requirements

As a further academic integrity control, students may be selected for a 15 minutes individual oral examination of their written assessment submissions.

Any student identified, either during the current semester or in retrospect, as having used ghost-writing services will be investigated under the University's Academic Misconduct Rule.

Class Schedule

Week/Session	Summary of Activities	Assessment
1	The Need for Measure Theory
2	Probability Triples
3	Sequence of Random Variables and Independence
4	Limit and Tail Fields
5	Expectation and Integration	Assignment 1 (15%)
6	Inequalities and Convergence
7	Distribution of Random Variables
8	Some Limit Theorems
9	Weak Convergence
10	Characteristic Functions
11	Decomposition of Probability Laws	Assignment 2 (25%)
12	Conditional Probability and Expectation

Tutorial Registration

Tutorials will be available on campus, live through scheduled Zoom sessions and as pre-recorded videos. Information regarding enrolments for these options will be provided on Wattle during O-week, prior to the start of the semester.

Assessment Summary

Assessment task	Value	Due Date	Return of assessment	Learning Outcomes
Assignment 1	15 %	25/03/2022	01/04/2022	1,2
Assignment 2	25 %	20/05/2022	27/05/2022	3,4
Final Exam	60 %	02/06/2022	30/06/2022	1-4

* 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.

Participation

Course content delivery will take the form of three in-person on campus lectures weekly lectures (available via echo360 on Wattle) and weekly tutorials, delivered in hybrid format (on campus, live through scheduled Zoom sessions and as pre-recorded videos).

Examination(s)

Centrally scheduled examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information.

Assessment Task 1

Assignment 1

Students are presented with Assignment 1 in Week 4 (by March 18). Students have to submit Assignment 1 in Week 5 (by 5pm on Friday, March 25) via Turnitin on Wattle. Assignment 1 is compulsory and completed individually.

Value: 15% of the Final Raw Mark

Assessment Task 2

Assignment 2

Students are presented with Assignment 2 in Week 10 (by May 13). Students have to submit Assignment 2 in Week 11 (by 5pm on Friday, May 20) via Turnitin on Wattle. Assignment 2 is compulsory and completed individually.

Value: 25% of the Final Raw Mark

Assessment Task 3

Final Exam

The compulsory final exam assesses the students’ overall understanding of the learning outcomes in the course. As a result, the final exam will contain material from the entire semester. Students will be provided with further details regarding the exam no later than week 10.

The final exam will be 3 hours in duration, taken online via Wattle.

Value: 60% of the Final Raw Mark

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

You will be required to electronically sign a declaration as part of the submission of your assignment. Please keep a copy of the assignment for your records. The submission must be through Turnitin.

Hardcopy Submission

There are no hardcopy submissions in the course.

Late Submission

No late submission of assessment tasks will be permitted. If an assessment task is not submitted by the due date and time, a mark of 0 will be awarded.

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

The marked assignments will be returned online.

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.

Resubmission of Assignments

It will not be possible for assignments to be resubmitted.

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