MM506: Probability theory I (5 ECTS)

STADS: 13000601

Level
Bachelor course

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

Teacher responsible
Email: bentj@stat.sdu.dk

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

Comment:
Ubegrænset deltagerantal. 3. kvartal. Fælles undervisning med MM812.

Prerequisites:
None

Academic preconditions:
The students must know contents of the course MM517.

Course introduction
To give the students a solid introduction to the mathematical treatment of probability theory based on abstract measure- and integration theory. The course presents fundamental elements of probability theory as it evolved during the twentieth century.

Competencies:
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.
Having completed the course successfully, the students can be expected to

• have a fundamental understanding of the mathematical formulation of stochastic phenomena.

• be able to establish simple stochastic models for various phenomena observed in nature and society.

• have experience in performing basic probability calculations.

• be prepared for advanced courses in probability theory and its applications in both applied math. (mathematical finance, statistics etc.) and in pure math. (Banach spaces, operator algebras etc.).

Expected learning outcome
By the end of 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. The mathematical description of a stochastic experiment

2. Distributions on the positive integers.

3. Distributions on the reals.

4. Multi-dimensional observations: joint and marginal distributions.

5. Moments, mean and standard deviation.

6. The characteristic function.

7. Weak convergence of probability measures.

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, internal evaluation by teacher

(b) A 30 minutes oral exam. External examiner, grades according to the 7-point marking scale.

Reexamination after 4. quarter.

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

(a) Forelæsninger (25 timer).
(b) Eksaminatorier (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.