Course syllabus

Sannolikhetsteori
Probability Theory

FMSF05, 7,5 credits, G2 (First Cycle)

Valid for: 2016/17
Decided by: Education Board B
Date of Decision: 2016-03-28

General Information

Elective for: BME4, F4, F4-fm, I4, Pi4-fm
Language of instruction: The course will be given in English on demand

Aim

The course gives a deaper and extended knowledge of probability theory, useful for further studies in, e.g., extreme value theory and stochastic processes and their applications.

Learning outcomes

Knowledge and understanding
For a passing grade the student must

• be able to explain different concepts in stochastic convergence and how they relate to each other,
• be able to explain the concepts of characteristic and moment generating functions and how these functions can be used,
• be able to descibe the multi dimensional normal distribution and the invariance properties under, e.g., linear combinations and conditioning,
• be able to explain the definition and basic properties of the Poisson process.

Competences and skills
For a passing grade the student must

• show the ability to integrate knowledge from the different parts of the course when solving problems.

Contents

The course deapens and expands the basic knowledge in probability theory. Central moments in the course are transforms of distribution, conditional expectations, multidimensional normal distribution, and stochastic convergence. Further, the concept of stochastic processes is introduced by a fairly thourough treatment of the properties of the Poisson process.

Examination details

Grading scale: TH
Assessment: Written and oral exam and written assignment.

Parts
Code: 0116. Name: Examination.
Credits: 6,5. Grading scale: TH. Assessment: Written and oral exam
Code: 0216. Name: Assignment.
Credits: 1. Grading scale: UG. Assessment: Written assignment

Admission

Admission requirements:

• FMS012 Mathematical Statistics, Basic Course or FMS032 Mathematical Statistics, Basic Course or FMS035 Mathematical Statistics, Basic Course or FMS086 Mathematical Statistics or FMS140 Mathematical Statistics, Basic Course or FMSF20 Mathematical Statistics, Basic Course

The number of participants is limited to: No
The course overlaps following course/s: MASC01

Reading list

• Gut, A.: An Intermediate Course in Probability Theory. Springer, 1995.

Contact and other information

Director of studies: Studierektor Anna Lindgren, studierektor@matstat.lu.se
Course homepage: http://www.maths.lth.se/matstat/kurser/fmsf05/
Further information: The course is also given at the Faculty of Science with the code MASC01.