Syllabus for Probability Theory II

Learning outcomes

 

To give a theoretical basis and problem solving skills within the subject probability theory for further studies in the mathematical and statistical sciences.

On completion of the course, the student should be able to:

• account for and use the theory of multivariate probability distributions;
• carry out variable substitutions using the transformation theorem;
• use the theory of conditional distribution, expectation, and variance to do calculations with dependent random variables;
• manage characteristic functions and other transforms and account for their theoretical properties;
• use matrix based computational methods for the multivariate normal distribution and account for its most important properties;
• account for and use various modes of convergence for stochastic variables;
• use the fundamental limit theorems in probability theory, the Law of Large Numbers and the Central Limit Theorem, and account for relevant fields of application and limitations.  

Content

The basic concepts of probability theory.  Multi-dimensional stochastic variables, dependence, conditioning. Probabilistic  transform methods, stochastic sums, order statistics.  Convergence modes and concepts in probability. The Law of Large Numbers and the Central Limit Theorem.

 

 

Instruction

Lectures and problem solving sessions.

Assessment

Written examination at the end of the course combined with written assignments during the course according to instructions delivered at course start.

If there are special reasons for doing so, an examiner may make an exception from the method of assessment indicated and allow a student to be assessed by another method. An example of special reasons might be a certificate regarding special pedagogical support from the disability coordinator of the university.

Other directives

The course may not be included in higher education qualification together with Mathematical Statistics (1MS013) 15 credits.