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Probability Theory II

Course category: 
2nd year
Module code: 
Dr Sonia Mazzi


The aim of the module is to provide an introduction to the formal, measure-theoretic foundations of probability, with special attention to conditional expectation.

Learning objectives

At the end of the module you should be able to...

  • Understand the concept of a probability space.
  • Understand the formal definition o random variables and the construction of distributions of random variables.
  • Understand and be able to compute the expected value of a random variable.
  • Understand and apply the definition of conditional expectation of a random variable given a σ-field
  • Be introduced to the concept of stochastic process and be able to solve basic problems involving Markov chains and martingales.


  • Probability spaces and σ-fields.
  • Random variables and distributions .
  • σ-field generated by a random variable.
  • Expectation of a random variable.
  • Conditional Expectation of discrete random variables wrt σ-fields
  • Introduction to stochastic processes: Markov chains and martingales.

Recommended texts

I don't follow one single textbook, but here are some good books on the subject.

  • Chung, K.L. A Course in Probability Theory.
  • G. Grimmett and D. Stirzaker. Probability and random processes, Oxford.
  • Rosenthal, J.S. (2006). A first look at rigorous probability theory. Second edition. World Scientific.


  • Spring Term
  • 2 lectures per week
  • Weekly Seminar


Example: One and a half hour closed examination in week 1 Summer Term (90%), Coursework (10%). Note that coursework submitted after the advertised deadlines will be given a mark of zero.

Elective information

A second course on probability  theory.

Please check prerequisites carefully before asking to take this module as an elective.


Edited 9 Sep 2010 - 13:54 by admin

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