## Probability Theory

 Faculteit Science and Engineering Jaar 2022/23 Vakcode WBMA046-05 Vaknaam Probability Theory Niveau(s) propedeuse Voertaal Engels Periode semester II b ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Probability Theory
Leerdoelen At the end of the course, the student is able to:
1. explain the basic concepts of probability theory such as sample space and events in relation to axioms of probability such as the inclusion-exclusion formula.
2. solve basic combinatorial problems.
3. translate experimental settings into probability density/mass functions and cumulative distribution functions.
4. compute expectation and higher order moments either directly or by the moment-generating function.
5. derive basic properties of several standard probability distributions such as the multivariate Gaussian.
6. determine conditional distributions from a given joint distribution and to determine distributions as a transformation from a given distribution.
7. prove convergence in probability and in distribution from the Law of Large Numbers and the Central Limit Theorem.
Omschrijving Everyone has an intuitive idea of concepts such as ``chance'' and ``opportunity'';. We can for instance think of: a lottery, weather, stock prices, or the number of cars at a given time on a motorway. In this course we will formalize these ideas by defining ``probability''; as a mathematical object that satisfies certain axioms.

The aim of this course is to train the student in using the formal mathematical framework to derive certain properties of various stochastic concepts. In particular, we build up a general space, in which probability is used as a measuring tool. We introduce concepts such as probability density and expectation and derive various limit theorems.

On the other hand, we will see how our mathematical framework enables us to solve practical problems. In order to facilitate this, we will consider combinatorics and several standard probability densities.
Uren per week
Onderwijsvorm Hoorcollege (LC), Opdracht (ASM), Werkcollege (T)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE)
(The assessment takes place through homework assignments and written exam: If WE >=4.5, then Final = 0.1 x (HW1+HW2+HW3) + 0.7 x WE; If WE <4.5, then Final = WE; where HWi is homework grade for ith homework set, WE is the final written exam grade. The homework grades do not count for the re-exam.)
Vaksoort propedeuse
Coördinator Dr. G.F.Y. Bonnet
Docent(en) Dr. G.F.Y. Bonnet
Verplichte literatuur
Titel Auteur ISBN Prijs
Lecturer notes
Entreevoorwaarden Knowledge assumed: Calculus 1, Analysis.
Opmerkingen This course was registered last year with course code WIKR-06
Opgenomen in
Opleiding Jaar Periode Type
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