# 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: **

** 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