STATS 710 Probability Theory

Below description edited in year: 2011

Points: 15

Prereqs: STATS 310, 320 or 325

Textbooks: Recommended reading: "A First Course in Probability" by Sheldon Ross.

For Advice: Mark Holmes (Email: m.holmes@auckland.ac.nz | extn: 88679)

Taught: First Semester City

Website: STATS 710 website

This course will provide an introduction to probability theory, for graduate students pursuing either statistical or stochastic modeling tracks.

The course will cover

1. The axiomatic definition of probability, associated set theory, and concepts such as independence and conditional probability.
2. Random Variables and Vectors; expectation, characteristic functions and transformation of random variables.
3. Limit theorems: convergence in distribution, laws of large numbers, and the central limit theorem.
4. Additional topics as time permits, such as sequences of dependent random variables and Markov processes.

Topics studied include: Probability with sigma-fields and measurable spaces, the weak and strong laws of large numbers, characteristic functions, the Central Limit Theorem. Additional topics may include ergodic theory, stable distributions.

Disclaimer:
Although every reasonable effort is made to ensure accuracy, this information for the course year (2012), is provided as a general guide only for students and is subject to alteration. All students enrolling at the University of Auckland must consult its official document, the University of Auckland Calendar, to ensure that they are aware of and comply with all regulations, requirements and policies.