SF2940 Probability Theory 7.5 credits

Sannolikhetsteori

The overall purpose of the course is that the student should be well acquainted with basic concepts in probability theory, models and solution methods applied to real problems.

Show course information based on the chosen semester and course offering:

Offering and execution

No offering selected

Select the semester and course offering above to get information from the correct course syllabus and course offering.

Course information

Content and learning outcomes

Course contents *

The basic concepts of probability theory. Measurability and sigma algebras. Characteristic functions and generating functions. Convergence of probability distributions, the Central Limit Theorem. Convergence of random variables. The Law of Large Numbers. Multivariate Normal distributions. Conditional distributions. Stochastic processes: Random walks, Branching processes, Poisson processes. Wiener processes (Brownian motion).

Intended learning outcomes *

To pass the course, the student should be able to do the following:

  • define and apply basic concepts and methods of probability theory
  • use common probability distributions and analyse their properties (exponential distribution, multivariate normal distribution, etc.)
  • compute conditional probability distributions and conditional expectations
  • solve problems and compute limits of distributions by use of transforms (characteristic functions, generating functions)
  • define and use the properties of Stochastic processes, especially random walks, branching processes, the Poisson and Wiener process, applied to real problems
  • explain the concept of measurability and define and work with sigma algebras and construct probability measures on sample spaces

To receive the highest grade, the student should in addition be able to do the following:

  • Combine all the concepts and methods mentioned above in order to solve more complex problems.

Course Disposition

No information inserted

Literature and preparations

Specific prerequisites *

Basic knowledge in Mathematical Statistics, Fourier Analysis and Linear Algebra.

Recommended prerequisites

No information inserted

Equipment

No information inserted

Literature

Timo Koski: Probability and Random Processes. Lecture Notes, 2013 
utges av  Inst. för matematik, KTH. 

Kursmaterial från institutionen för matematik.

Examination and completion

Grading scale *

A, B, C, D, E, FX, F

Examination *

  • TEN1 - Examination, 7.5 credits, Grading scale: A, B, C, D, E, FX, F

Based on recommendation from KTH’s coordinator for disabilities, the examiner will decide how to adapt an examination for students with documented disability.

The examiner may apply another examination format when re-examining individual students.

Opportunity to complete the requirements via supplementary examination

No information inserted

Opportunity to raise an approved grade via renewed examination

No information inserted

Examiner

Boualem Djehiche

Further information

Course web

Further information about the course can be found on the Course web at the link below. Information on the Course web will later be moved to this site.

Course web SF2940

Offered by

SCI/Mathematics

Main field of study *

Mathematics

Education cycle *

Second cycle

Add-on studies

No information inserted

Contact

Boualem Djehiche (boualem@kth.se)

Ethical approach *

  • All members of a group are responsible for the group's work.
  • In any assessment, every student shall honestly disclose any help received and sources used.
  • In an oral assessment, every student shall be able to present and answer questions about the entire assignment and solution.