## Probability Theory

 Faculteit Science and Engineering Jaar 2019/20 Vakcode WIKR-06 Vaknaam Probability Theory Niveau(s) propedeuse Voertaal Engels Periode semester II b ECTS 5 Rooster rooster.rug.nl

Uitgebreide vaknaam Probability Theory
Leerdoelen After the course:
1. The student can reproduce basic concepts such as sample space and events in relation to axioms of probability such as the inclusion-exclusion formula.
2. The student can solve basic combinatorial problems.
3. The student is able to translate experimental settings into probability density and cumulative distribution functions
4. The student can compute expectation and higher order moments either directly or by the moment-generating function
5. The student is able to derive basic properties of several standard probability distributions such as the multivariate Gaussian.
6. The student is able to determine conditional distributions from a given joint distribution and to determine distributions as a transformation from a given distribution
7. The student can prove convergence in probability and in distribution from the Law of Large Numbers and the Central Limit Theorem

The course contributes to the following transferable skills:

1. conducting mathematical proofs (more generally, scientific reasoning)
2. problem solving
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), Werkcollege (T)
Toetsvorm Opdracht (AST), Schriftelijk tentamen (WE)
(ssessment take place through homework assignments and written exam: Final = 0.1 x (HW1+HW2+HW3) + 0.7 x ET, where HWi is homework grade for ith homework set, ET final exam grade) only if ET >=4.5 otherwise Final = ET, where HWi is homework grade for ith homework set, ET final exam grade. The homework grades do not count for the re-exam.)
Vaksoort propedeuse
Coördinator C.P. Hirsch
Docent(en) C.P. Hirsch
Verplichte literatuur
Titel Auteur ISBN Prijs
Lecturer notes
Elementary Probability - 2nd edition David Stirzaker 9780511755309
Entreevoorwaarden the course prepares for the second year course Statistics
Opmerkingen
Opgenomen in
Opleiding Jaar Periode Type
BSc Courses for Exchange Students: Mathematics 19-20 - semester II b
BSc Mathematics and Physics (double degree) 1 semester II b verplicht
BSc Mathematics: General Mathematics  ( Major track General Mathematics) 1 semester II b verplicht
BSc Mathematics: Probability and Statistics 1 semester II b verplicht
BSc Technische Wiskunde 1 semester II b verplicht