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732A63 Probability theory

Course information

Course contents:

The course aims to provide the student with a solid understanding of basic results and methods in probability. The topics covered include: major classes of probability distributions, multivariate random variables, conditioning, transforms, order statistics, multivariate normal distributions, and convergence concepts.

Course organisation:

The teaching is comprised of lectures and seminars.
The lectures are devoted to presentations of theories, concepts, and methods.
The seminars are devoted to presentation and discussion of assignments.


A written final exam. Active participation in the seminars gives bonus points to the exam. See further under examination.

Course literature:

Gut, A. An intermediate course in probability. 2nd ed. Springer-Verlag, New York, 2009. ISBN 978-1-4419-0161-3
Misprints and corrections may be read at http://www2.math.uu.se/~allan/81misprints.pdf

Course start:

The time before the first lecture should be spent on self-study to fresh up your knowledge in probability theory from previous course(s). Before the first lecture, students should be familiar with at least the following concepts:

  • Probabilities of events
  • The basic laws of probabilities
  • Bayes theorem for events
  • Random variables
  • Probability distributions
  • The most common distributions: normal, chi-square, student t, binomial and poisson.
  • Expected value and variance
  • Covariance and correlation
  • Linear regression


Basic skills in probability theory corresponding to an introductory course in statistics.
Calculus (corresponding to a first course)

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Last updated: 2020-12-22