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: bentj@stat.sdu.dk

Timetable
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Comment:
Ubegrænset deltagerantal. 3. kvartal. Fælles undervisning med MM506.

Prerequisites:
None

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

Course introduction
The aim of the course is to give the participants a solid mathematical introduction to probability theory, based on the measure theory and integration. The participants will learn the fundamental concepts of probability theory, developed through the 20. century.

Expected learning outcome
By the end of the course the student will be able to:
- formulate central results of probability theory within the syllabus of the course and give detailed and stringent proofs of them.
- use the theory to solve problems within the syllabus of the course.
- be familiar with the different forms of convergence of sequences of stochastic variables and apply the results.
- relate and apply the results of the course to other areas of mathematics

Subject overview
1. The concept of probability and the mathematical description of a stochastic experiment. Stochastic variables.
2. Simple combinatoric experiments. The normal distribution and other standard distributions.
3. The Borel-Cantelli lemma and its applications.
4. Independence.
5. Moments, mean value and variance of stochastic variables. Chebyshev's inequality, Jensen's inequality. Convergence in probability.
6. The characteristic function and its properties.
7. Weak convergence of probability measures.
8. The central limit theorem.

Literature

• Meddeles ved kursets start..

Website
This course uses e-learn (blackboard).

Prerequisites for participating in the exam
None

Assessment and marking:


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

Forelæsninger: 25 timer
Eksaminatorietimer/opgaveregning: 25 timer
Educational activities

Language
This course is taught in English, if international students participate. Otherwise the course is taught in Danish.

Course enrollment
See deadline of enrolment.

Tuition fees for single courses
See fees for single courses.