MM835: Probability theory (10 ECTS)

STADS: 13013301

Level
Master's level course

Teaching period
The course is offered in the autumn semester.

Teacher responsible
Email: bentj@imada.sdu.dk

Additional teachers
gabe@imada.sdu.dk

Timetable
Show entire timetable
Show personal time table for this course.

Comment:
Ubegrænset antal. Undervises fælles med MM544, Sandsynlighedsteori.

Prerequisites:
None

Academic preconditions:
MM543 Mål- integralteori og Banachrum forudsættes kendt.

Course introduction
To give the students a solid introduction to the mathematical treatment of probability theory.

Qualifications
Probability theory is the mathematical foundation for theoretical statistics, and it has also found numerous applications in other branches of mathematics, e.g. functional analysis.

Expected learning outcome

• reproduce definitions in probability theory within the scope of the course’s syllabus
• reproduce results in probability theory, together with their proofs, within the scope of the course’s syllabus
• apply the theory to solve problems in probability theory
• relate the results within the scope of the course’s syllabus to each other

Subject overview
random variables, probability measures, distribution functions, expectation, independence, characteristic functions, the normal and multivariate normal distribution, convergence of random variables, central limit theorems, conditional expectation, martingales

Literature

Meddeles ved kursets start

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:

1. Report and oral examination. The report is evaluated as a part of the oral exam. Evaluated by external censorship by the Danish 7 mark scale (10 ECTS).

Expected working hours
The teaching method is based on three phase model.
Intro phase: 50 hours
Skills training phase: 28 hours, hereof:
 - Tutorials: 28 hours

Educational activities Study phase: 10 hours

Language
This course is taught in Danish or English, depending on the lecturer. However, if international students participate, the teaching language will always be English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.