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.
Examination:
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
Prerequisities:
Basic skills in probability theory corresponding to an
introductory course in statistics.
Calculus (corresponding to a
first course)
Useful material:
- Table with common integrals
- Table with common mathematical and statistical formulas
- 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.
- CRAN list of distributions in R.
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Last updated: 2020-12-22