# 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, 10 February 2020
Responsible department
Department of Mathematics

## Entry requirements

Probability 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 transforms, such as moment-generating functions, and to account for their theoretical properties;
• account for the most important properties for multidimensional normal distributions;
• account for different types of convergence for stochastic variables as well as The Law of Large Numbers and The Central Limit Theorem.

## Content

The basic concepts of the probability theory, multidimensional stochastic variables, conditioning, transforms, 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.

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.