STATS 313 : Advanced Topics in Probability
2022 Semester Two (1225) (15 POINTS)
Capabilities Developed in this Course
|Capability 1:||Disciplinary Knowledge and Practice|
|Capability 2:||Critical Thinking|
|Capability 3:||Solution Seeking|
|Capability 4:||Communication and Engagement|
|Capability 5:||Independence and Integrity|
- Apply the main results and techniques of probability theory. (Capability 1, 3 and 4)
- Solve a variety of problems in probability using rigorous mathematical arguments. (Capability 1, 2, 3, 4 and 5)
- Perform calculations and work effectively with probability measures, conditional expectations as random variables, and generating functions. (Capability 1, 3 and 4)
- Apply the classical limit theorems, convergence theorems and main inequalities of probability. (Capability 1, 2, 3 and 4)
- Distinguish between and determine the various types of convergence for random variables. (Capability 1, 2, 3 and 4)
- Develop rigorous arguments and clear explanations, as appropriate. (Capability 1, 2, 3, 4 and 5)
|Final Exam||50%||Individual Examination|
|Assessment Type||Learning Outcome Addressed|
Topics may include: Probability measures, event spaces, sigma-algebras, Borel sets, continuity of probability. The Fundamental model of uniform probability measure on [0,1]. Independence. Borel-Cantelli Lemmas. Random variables. Expectation. Monotone and Dominated Convergence Theorems. Inequalities for expectations. Conditional expectation as a random variable. Generating functions, including Characteristic functions and Laplace transforms. Convergence of generating functions. Types of convergence. Sequences of independent random variables. Weak and Strong Laws of Large Numbers, and the Central Limit Theorem. Other topics, models or applications of probability.
For this course, in each teaching week you can typically expect 3 hours of lectures, a 1 hour tutorial, 1-3 hours of reading and thinking about the content, and 3-5 hours of work on assignments.
Lectures will be available as recordings. Other learning activities such as tutorials will not typically be available as recordings, but the course may additionally include live online tutorials. Online Q&A help will also be available via Piazza on the course Canvas site. All course materials will be made available online via Canvas.
Coursework may be submitted online via Canvas.
The activities for the course are scheduled as a standard weekly timetable.
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
Please remember that the recording of any class on a personal device requires the permission of the instructor.
During the course Class Representatives in each class can take feedback to the staff responsible for the course and staff-student consultative committees.
At the end of the course students will be invited to give feedback on the course and teaching through a tool called SET or Qualtrics. The lecturers and course co-ordinators will consider all feedback.
Your feedback helps to improve the course and its delivery for all students.
The University of Auckland will not tolerate cheating, or assisting others to cheat, and views cheating in coursework as a serious academic offence. The work that a student submits for grading must be the student's own work, reflecting their learning. Where work from other sources is used, it must be properly acknowledged and referenced. This requirement also applies to sources on the internet. A student's assessed work may be reviewed against online source material using computerised detection mechanisms.
Class representatives are students tasked with representing student issues to departments, faculties, and the wider university. If you have a complaint about this course, please contact your class rep who will know how to raise it in the right channels. See your departmental noticeboard for contact details for your class reps.
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If your ability to complete assessed coursework is affected by illness or other personal circumstances outside of your control, contact a member of teaching staff as soon as possible before the assessment is due.
If your personal circumstances significantly affect your performance, or preparation, for an exam or eligible written test, refer to the University’s aegrotat or compassionate consideration page https://www.auckland.ac.nz/en/students/academic-information/exams-and-final-results/during-exams/aegrotat-and-compassionate-consideration.html.
This should be done as soon as possible and no later than seven days after the affected test or exam date.
In the event of an unexpected disruption, we undertake to maintain the continuity and standard of teaching and learning in all your courses throughout the year. If there are unexpected disruptions the University has contingency plans to ensure that access to your course continues and course assessment continues to meet the principles of the University’s assessment policy. Some adjustments may need to be made in emergencies. You will be kept fully informed by your course co-ordinator/director, and if disruption occurs you should refer to the university website for information about how to proceed.
The delivery mode may change depending on COVID restrictions. Any changes will be communicated through Canvas.
Student Charter and Responsibilities
The Student Charter assumes and acknowledges that students are active participants in the learning process and that they have responsibilities to the institution and the international community of scholars. The University expects that students will act at all times in a way that demonstrates respect for the rights of other students and staff so that the learning environment is both safe and productive. For further information visit Student Charter https://www.auckland.ac.nz/en/students/forms-policies-and-guidelines/student-policies-and-guidelines/student-charter.html.
Elements of this outline may be subject to change. The latest information about the course will be available for enrolled students in Canvas.
In this course students may be asked to submit coursework assessments digitally. The University reserves the right to conduct scheduled tests and examinations for this course online or through the use of computers or other electronic devices. Where tests or examinations are conducted online remote invigilation arrangements may be used. In exceptional circumstances changes to elements of this course may be necessary at short notice. Students enrolled in this course will be informed of any such changes and the reasons for them, as soon as possible, through Canvas.