STATS 710 Probability Theory

Below description edited in year: 2018

Points: 15

Prereqs: STATS 310 or 320 or 325, (or MATHS 332 and permission of lecturer)

Credit: Final exam 60%, assignments 40%.

Textbooks: "Knowing the Odds: An Introduction to Probability" by John Walsh

For Advice: Simon Harris (Email: simon.harris@auckland.ac.nz | extn: 81109), Jesse Goodman (Email: jesse.goodman@auckland.ac.nz | extn: 88646)

Taught: Second Semester City

Website: STATS 710 website

This course will provide an introduction to probability theory, and is recommended for graduate students interested in statistical theory, stochastic modelling, quantitative finance, probability, statistical physics, and analysis. The course will cover: 1. The axiomatic definition of probability, associated set theory, and independence. 2. Random Variables and Vectors, expectation, conditional expectation, moments, and characteristic functions. 3. Limit theorems, including the “fundamental theorems of statistics” (the law of large numbers, and the central limit theorem). 4. Other topics chosen by the instructors.

Topics studied include: Probability with sigma-fields and measurable spaces. Borel-Cantelli Lemmas and 0-1 laws. Random variables, expectation and condition expectation. Moment generating functions and characteristic functions. Sequences of independent random variables, the Law of Large Numbers, and the Central Limit Theorem.

Disclaimer:
Although every reasonable effort is made to ensure accuracy, this information for the course year (2018), 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.