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.

  • Education cycle

    Second cycle
  • Main field of study

    Mathematics
  • Grading scale

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

Course offerings

Autumn 19 CINEK m.fl. for programme students

Autumn 18 CINEK m.fl. for programme students

Autumn 18 Doktorand for single courses students

  • Periods

    Autumn 18 P1 (7.5 credits)

  • Application code

    10125

  • Start date

    27/08/2018

  • End date

    26/10/2018

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places *

    1 - 1

    *) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.

  • Course responsible

    Boualem Djehiche <boualem@kth.se>

  • Teacher

    Boualem Djehiche <boualem@kth.se>

  • Target group

    For doctoral students at KTH

Autumn 18 Doktorand for single courses students

  • Periods

    Autumn 18 P1 (7.5 credits)

  • Application code

    10141

  • Start date

    27/08/2018

  • End date

    26/10/2018

  • Language of instruction

    English

  • Campus

    KTH Campus

  • Tutoring time

    Daytime

  • Form of study

    Normal

  • Number of places *

    1 - 1

    *) The Course date may be cancelled if number of admitted are less than minimum of places. If there are more applicants than number of places selection will be made.

  • Course responsible

    Boualem Djehiche <boualem@kth.se>

  • Teacher

    Boualem Djehiche <boualem@kth.se>

  • Target group

    For doctoral students at KTH

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 main content

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).

Eligibility

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

Literature

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

Kursmaterial från institutionen för matematik.

Examination

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

Offered by

SCI/Mathematics

Contact

Boualem Djehiche (boualem@kth.se)

Examiner

Boualem Djehiche <boualem@kth.se>

Version

Course syllabus valid from: Spring 2013.
Examination information valid from: Autumn 2007.