Probability Theory
Sannolikhetsteori

FMSF05, 7.5 credits, G2 (First Cycle)

Valid for: 2024/25
Faculty: Faculty of Engineering LTH
Decided by: PLED I
Date of Decision: 2024-04-16
Effective: 2024-05-08

General Information

Depth of study relative to the degree requirements: First cycle, in-depth level of the course cannot be classified
Elective for: BME4, F4, F4-fm, I4, Pi4
Language of instruction: The course will be given in English

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 - (U, 3, 4, 5) - (Fail, Three, Four, Five)
Assessment: Written exam.

The examiner, in consultation with Disability Support Services, may deviate from the regular form of examination in order to provide a permanently disabled student with a form of examination equivalent to that of a student without a disability.

Modules
Code: 0120. Name: Examination.
Credits: 7.5. Grading scale: TH - (U, 3, 4, 5). Assessment: Written exam

Admission

Admission requirements:

• FMSF20 Mathematical Statistics, Basic Course or FMSF25 Mathematical Statistics - Complementary Project or FMSF32 Mathematical Statistics or FMSF45 Mathematical Statistics, Basic Course or FMSF50 Mathematical Statistics, Basic Course or FMSF55 Mathematical Statistics, Basic Course or FMSF70 Mathematical Statistics or FMSF75 Mathematical Statistics, Basic Course or FMSF80 Mathematical Statistics, Basic Course

Reading list

• Gut, A: An Intermediate Course in Probability Theory - Second Edition. Springer, 2010, ISBN: 978-1-4899-8446-3.

Contact

Director of studies: Johan Lindström, studierektor@matstat.lu.se
Course administrator: Susann Nordqvist, expedition@matstat.lu.se
Course homepage: https://www.maths.lu.se/utbildning/civilingenjoersutbildning/matematisk-statistik-paa-civilingenjoersprogram/

Further information