STATS 710 : Probability Theory
2020 Semester Two (1205) (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 sigma-algebras, 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||60%||Individual Examination|
|Assessment Type||Learning Outcome Addressed|
Topics include: Probability measures, event spaces, sigma-algebras, Borel sets, continuity of probability. The Fundamental model of uniform probability measure on [0,1] and Lebesgue-Borel Theorem. Independence. Borel-Cantelli Lemmas. Random variables. Expectation. Monotone and Dominated Convergence Theorems. Inequalities for expectations. Conditional expectation as a random variable. Discrete time martingales. 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.
This course is a standard 15 point course and students are expected to spend 10 hours per week involved in each 15 point course that they are enrolled in.
For this course, you can expect 3 hours of lectures, a 1 hour tutorial, 2 hours of reading and thinking about the content and 4 hours of work on assignments and/or test preparation.
Course materials are made available in a learning and collaboration tool called Canvas which also includes reading lists and lecture recordings (where available).
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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.
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.
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 you may be asked to submit your 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. The final decision on the completion mode for a test or examination, and remote invigilation arrangements where applicable, will be advised to students at least 10 days prior to the scheduled date of the assessment, or in the case of an examination when the examination timetable is published.