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, 01 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, largesample testing and Bayesian methods. Finally you will verify important convergence properties of the expectationmaximisation (EM) algorithm. By doing this unit you will become familiar with many of the theoretical building blocks that are required for any indepth study in probability or mathematical statistics.
Unit details and rules
Academic unit  Mathematics and Statistics Academic Operations 

Credit points  6 
Prerequisites
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None 
Corequisites
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None 
Prohibitions
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STAT4528 
Assumed knowledge
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STAT3X23 or equivalent: that is, a sound working and theoretical knowledge of statistical inference 
Available to study abroad and exchange students  Yes 
Teaching staff
Coordinator  Michael Stewart, michael.stewart@sydney.edu.au 

Lecturer(s)  Michael Stewart, michael.stewart@sydney.edu.au 
Qiying Wang, qiying.wang@sydney.edu.au 