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Year - 2020

Probability Theory lays the theoretical foundations that underpin the models we use when analysing phenomena that involve chance. This unit introduces the students to modern probability theory and applies it to problems in mathematical statistics. You will be introduced to the fundamental concept of a measure as a generalisation of the notion of length and Lebesgue integration which is a generalisation of the Riemann integral. This theory provides a powerful unifying structure that bring together both the theory of discrete random variables and the theory of continuous random variables that were introduce to earlier in your studies. You will see how measure theory is used to put other important probabilistic ideas into a rigorous mathematical framework. These include various notions of convergence of random variables, 0-1 laws, and the characteristic function. You will then synthesise all these concepts to establish the Central Limit Theorem and also verify important results in Mathematical Statistics. These involve exponential families, efficient estimation, large-sample testing and Bayesian methods. Finally you will verify important convergence properties of the expectation-maximisation (EM) algorithm. By doing this unit you will become familiar with many of the theoretical building blocks that are required for any in-depth study in probability or mathematical statistics.

Classes

3 x 1hr lectures/week, 1 x 1hr tutorial or laboratory class/week

Assessment

12 x weekly homework (40%), final exam (60%)

Assumed knowledge

STAT3X23 or equivalent: that is, a sound working and theoretical knowledge of statistical inference.

STAT4528

Faculty: Science

Semester 1

24 Feb 2020

Department/School: Mathematics and Statistics Academic Operations

Study Mode: Normal (lecture/lab/tutorial) day

Census Date: 31 Mar 2020

Unit of study level: Honours

Credit points: 6.0

EFTSL: 0.125

Available for study abroad and exchange: Yes

Faculty/department permission required? No

Location

Camperdown

More details

HECS Band: 2

Leadership for good starts here

ABN: 15 211 513 464

CRICOS Number: 00026A

TEQSA: PRV12057