# Probability Theory II

5 credits

Syllabus, Bachelor's level, 1MS036

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, 9 February 2023
Responsible department
Department of Mathematics

## Entry requirements

60 credits including 20 credits in mathematics. Participation in Probability Theory I or Probability and Statistics. Participation in Several Variable Calculus M, Several Variable Calculus or Several Variable Calculus Limited Version. Participation in Linear Algebra 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.