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 STAT3006, 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 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 probability theory techniques;
3. Demonstrate mathematical reasoning through analyzing, proving and explaining concepts from probability theory; and
4. Apply 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 20 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

Final Exam

·        two sheets of A4 paper with handwritten notes only on both sides

·        paper-based English language dictionary, no approval required (must be clear OF ALL annotations)

·        calculator (any - programmable or not)

Required Resources

Prescribed Text

       Jeffrey S. Rosenthal (2006) A First Look at Rigorous Probability Theory. 2nd Edition. World Scientific, Singapore

Available at loan desk for 2 hour loan at Hancock library and University Book Shop.

Recommended Resources

Recommended Reading

George G Roussas (2014) An Introduction to Measure-Theoretic Probability. 2nd Edition. Academic Press

Rick Durrett (2010) Probability: Theory & Examples. 4th Edition. Cambridge. University Press, Cambridge.

Davar Khoshnevisan (2007) Probability. American Mathematical Society. Providence,RI.

Sidney I. Resnick (2015) A probability path. Reprint of the fifth (2005) printing of the 1999 original. Birkhaeuser/Springer, New York.

Daniel W. Stroock (2013) Mathematics of Probability. American Mathematical Society, Providence.

David Williams (1991) Probability with Martingales. Cambridge University Press, Cambridge.

Available via the University library.

Staff Feedback

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

·        Written comments, both individually and to the whole class.

·        Verbal comments to the whole class

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). The feedback given in these surveys is anonymous and provides the Colleges, University Education Committee and Academic Board with opportunities to recognise excellent teaching, and opportunities for improvement. The Surveys and Evaluation website provides more information on student surveys at ANU and reports on the feedback provided on ANU courses.

Other Information

Consultation time will be finalised at the start of the semester.

Scaling

Your 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 formula, 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 the scaled mark of that student), and may be either up or down.

Referencing Requirements

Appropriate referencing will be necessary for the Assignments. For more information see:  http://www.anu.edu.austudents/learning-development/academic-integrity/how-referencing- works

Extensions and Penalties

No submission of assessment tasks without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 will be awarded.

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/

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
6	Inequalities and Convergence
7	Distribution of random variables
8	Some Limit theorems
9	Weak Convergence
10	Characteristic Functions
11	Decomposition of Probability Laws
12	Conditional Probability and Expectation

Assessment Summary

Assessment task	Value	Learning Outcomes
Final Exam (compulsory)	100 %	1,2,3,4,5,6,7,8,9,10,11,12

* 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 Misconduct Rule before the commencement of their course. Other key policies and guidelines include:

• Student Assessment (Coursework) Policy and Procedure
• Special Assessment Consideration Policy and General Information 
• Student Surveys and Evaluations
• Deferred Examinations
• Student Complaint Resolution Policy and Procedure

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 ANU Online 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.

Examination(s)

As a further academic integrity control, students may be selected for a 15 minute 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.

Centrally administered examinations through Examinations, Graduations & Prizes will be timetabled prior to the examination period. Please check ANU Timetabling for further information. Exam scripts will not be returned.

Assessment Task 1

Final Exam (compulsory)

The compulsory final exam assesses the students’ overall learning outcomes.

The final exam consist of 15 min of reading time and 3 hours of writing time.

Value: 100% of the Final Raw Mark

Academic Integrity

Academic integrity is a core part of the ANU culture as a community of scholars. At its heart, academic integrity is about behaving ethically, committing to honest and responsible scholarly practice and upholding these values with respect and fairness.

The ANU commits to assisting all members of our community to understand how to engage in academic work in ways that are consistent with, and actively support academic integrity. The ANU expects staff and students to be familiar with the academic integrity principle and Academic Misconduct Rule, uphold high standards of academic integrity and act ethically and honestly, to ensure the quality and value of the qualification that you will graduate with.

The Academic Misconduct Rule is in place to promote academic integrity and manage academic misconduct. Very minor breaches of the academic integrity principle may result in a reduction of marks of up to 10% of the total marks available for the assessment. The ANU offers a number of online and in person services to assist students with their assignments, examinations, and other learning activities. Visit the Academic Skills website for more information about academic integrity, your responsibilities and for assistance with your assignments, writing skills and study.

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. Unless an exemption has been approved by the Associate Dean (Education) submission must be through Turnitin.

Hardcopy Submission

For some forms of assessment (hand written assignments, art works, laboratory notes, etc.) hard copy submission is appropriate when approved by the Associate Dean (Education). Hard copy submissions must utilise the Assignment Cover Sheet. Please keep a copy of tasks completed for your records.

Late Submission

No submission of assessment tasks without an extension after the due date will be permitted. If an assessment task is not submitted by the due date, a mark of 0 will be awarded.

Referencing Requirements

Accepted academic practice for referencing sources that you use in presentations can be found via the links on the Wattle site, under the file named “ANU and College Policies, Program Information, Student Support Services and Assessment”. Alternatively, you can seek help through the Students Learning Development website.

Returning Assignments

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

Assignments may not 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 Diversity 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