| Code |
14778
|
| Year |
2
|
| Semester |
S1
|
| ECTS Credits |
6
|
| Workload |
TP(60H)
|
| Scientific area |
Mathematics
|
|
Entry requirements |
Differential and integral calculus.
|
|
Learning outcomes |
To develop probability models for variables on measurable spaces of different dimensions; identify and apply the properties of probability laws in problem solving; identify and apply the various modes of stochastic convergence.
|
|
Syllabus |
1. Probability spaces: axiomatic, conditional probability and independence in a family of events.
2. Laws of probability on IR: classification and integration.
3. Probability laws on IRn: independent random variables, transformation of random vectors, moments, moment generating function and conditional distributions.
4. Normal vectors: characterization, independence and correlation.
5. Stochastic convergences: convergence in law, functional convergences, laws of large numbers and the central limit theorem.
|
|
Main Bibliography |
Main: Gonçalves, E. e Lopes, M.N. (2013) Probabilidades, Escolar Editora.
Additional:
Kallenberg, O. (1997). Foundations of Modern Probability, Springer.
Resnick, S.I. (1999). A Probability Path, Birkh ¨auser.
|
|
Teaching Methodologies and Assessment Criteria |
The classes will be fundamentally theoretical-practical in nature, combining the exposure of syllabus, with their discussion and application in practical examples. Previously provided notes/slides will be provided for the student to do a preliminary study and in class will be made an exhibition of the main contents.
The more theoretical contents will be presented with the use of practical and concrete examples.
The evaluation of this UC includes holding two written tests and five mini-tests to be performed on the computer.
|
|
Language |
Portuguese. Tutorial support is available in English.
|