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
Group |
Type |
Day |
Time |
Classroom |
Weeks |
Comment |
Common |
I |
Monday |
10-12 |
U20 |
05,07-11 |
|
Common |
I |
Monday |
10-12 |
U74 |
06 |
|
Common |
I |
Thursday |
12-14 |
U49D |
05-10 |
|
S1 |
TE |
Tuesday |
14-16 |
U49B |
05-11 |
|
S1 |
TE |
Friday |
12-14 |
U35 |
06-11 |
|
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Revison of timetable:
: LOKALEÆNDRING MANDAG KL. 10-12 I UGE 6.
Comment:
Identisk med MM506
Ubegrænset deltagerantal. 3. kvartal.
Prerequisites:
None
Academic preconditions:
The content of the course MM517, Measure and Integration must be known
Course introductionThe 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 outcomeBy 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 overview1. 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.
LiteratureMeddeles ved kursets start.
Syllabus
See syllabus.
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.