# Probability Theory II

5 credits

Syllabus, Bachelor's level, 1MS036

A revised version of the syllabus is available.
Code
1MS036
Education cycle
First cycle
Main field(s) of study and in-depth level
Mathematics G2F
Fail (U), Pass (3), Pass with credit (4), Pass with distinction (5)
Finalised by
The Faculty Board of Science and Technology, 24 April 2013
Responsible department
Department of Mathematics

## Entry requirements

Probability Theory I and Inference Theory I.

## Learning outcomes

To give a theoretical basis within the subject Probability theory for further studies in Mathematical statistics.

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

• carry out variable exchange calculations for multidimensional distributions and account for the theorem that these calculations build on;
• use and account for the concept of conditioning;
• carry out calculations with characteristic functions and be able to account for the theoretical properties of these functions;
• account for the most important properties for multidimensional normal distributions;
• prove the main clauses of the probability theory (The Law of Large Numbers and The Central Limit Theorem).

## Content

The basic concepts of the probability theory, multidimensional stochastic variables, conditioning, characteristic functions, convergence concepts, 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.

## Other directives

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