Probability Theory, 7.5 credits

Learning outcomes

After completed studies, the student should be able to

• use the theory of measurable functions to analyse and solve theoretical problems in probability theory, and
• communicate reasoning and solutions in a clear, structured and mathematically correct way, both in oral and written form.

Content

Sigma algebras, measurable sets, Lebesgue measure, measurable functions, events, stochastic variables, dependence, expected value, convergence (almost sure, in mean, in probability, and in distribution), strong law of large numbers, Borel-Cantelli, characteristic functions, the central limit theorem.

Examinations and grades

Examination, 7.5 credits (Code: A001)
Grades used are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

According to the Higher Education Ordinance, Chapter 6, Section 18, a grade is to be awarded on the completion of a course, unless otherwise prescribed by the university. The university may determine which grading system is to be used. The grade must be determined by a teacher specifically nominated by the university (the examiner).

In accordance with university regulations on grading systems for first and second-cycle courses and study programmes (Vice-Chancellor’s decision ORU 2018/00929), one of the following grades is to be used: fail (U), pass (G) or pass with distinction (VG). For courses included in an international master’s programme (60 or 120 credits) or offered to the university’s incoming exchange students, the A to F grading scale is to be used. The vice-chancellor, or a person appointed by them, may decide on exceptions from this provision for a specific course, if there are special grounds for doing so.

The grades used on this course are Fail (F), Sufficient (E), Satisfactory (D), Good (C), Very Good (B) or Excellent (A).

Comments on grades

Grading scale A-F according to the vice-rector's decision 2019-11-12 case no: ORU 06367/2019.

Modes of assessment

• Examination (code A001): Written assignment and oral examination

For students with a documented disability, the university may approve applications for adapted or other modes of assessment.

For further information, see the university's local examination regulations.

Specific entry requirements

Foundations of Analysis, 7.5 credits, Statistics, Statistical Theory, Intermediate Course, 15 credits and Abstract Algebra, 7.5 credits.

For further information, see the university's admission regulations.

Other provisions

All or part of the course may be given in English.

Students who have been admitted to and registered on a course have the right to receive tuition and/or supervision for the duration of the time period specified for the particular course to which they were accepted (see, the university's admission regulations (in Swedish)). After that, the right to receive tuition and/or supervision expires.

Reading list and other learning resources

Required Reading

Durrett, Rick (Latest edition)
Probability, Theory and Examples
Cambridge University Press

Häggström, Olle and Lindvall, Torgny (1999)
Sannolikhetsteorins grunder
Chalmers: http://www.math.chalmers.se/~olleh/kompendium2.ps