MM812: Probability Theory I (5 ECTS)

STADS: 13004401

Level
Master's level course

Teaching period
The course is offered in the spring semester.
3rd quarter

Teacher responsible
Email: yuri.goegebeur@stat.sdu.dk

Additional teachers
mosma@imada.sdu.dk

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

Comment:
Ubegrænset deltagerantal.Fælles undervisning med MM506 Sandsynlighedsteori I

Prerequisites:
None

Academic preconditions:
The content of the course MM517, Measure and Integration must be known

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
After successfully having followed the course, the student will be able to:
- 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
- explain, with proofs, the different modes of convergence of sequences of stochastic variables, and how they are related to each other

Subject overview
1. Properties of probability distributions

2. Characteristic functions

3. Moments and cumulants

4. Convergence in distribution and in probability

5. Central limit theorems

6. Approximations to the distributions of more general statistics

Literature

Meddeles ved kursets start.

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:
a) A number of mandatory assignments during the course. These assignments must be passed in order to take the exam. Pass/Fail, intermal evaluation by teacher

b) A 30 minutes oral exam. External examiner, grades according to the 7 mark scale

Reexamination after 4. quarter 

Expected working hours
The teaching method is based on three phase model.

Forelæsninger: 28 timer
Eksaminatorietimer/opgaveregning: 14 timer
Educational activities

Language
This course is taught in English.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.