732A40 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

Examination:

A written final exam. See further under exam.

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 course starts in late August, but the first lecture will not be held until Wednesday September 3, 2015 at 3.15 in Thomas Bayes
The time before the first lecture should be spent on self-study to fresh up your knowledge in probability theory from previous course(s). My slides (in English) from our third-year bachelor course may be of some help (Slides 1-6 are about probability theory)
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

Prerequisities:

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

Useful material:

• The course material is maintained on GitHub. Here is the repository for the course.
• Table with common integrals
• Exams with solutions from a course at KTH. But note that not all exam questions are relevant for this course, in particular the ones for stochastic processes (which we do not cover in this course).
• Wikipedia's page on complex numbers is quite good and compact.
• For whatever it is worth, here are my code snippets for the course.
• CRAN list of distributions in R.

Page responsible: Mattias Villani
Last updated: 2014-09-04