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2020/2021

Probability and stochastic modelling

Code: 100104 ECTS Credits: 8
Degree Type Year Semester
2500149 Mathematics OB 3 1
The proposed teaching and assessment methodology that appear in the guide may be subject to changes as a result of the restrictions to face-to-face class attendance imposed by the health authorities.

Contact

Name:
Maria Jolis Giménez
Email:
Maria.Jolis@uab.cat

Use of Languages

Principal working language:
catalan (cat)
Some groups entirely in English:
No
Some groups entirely in Catalan:
Yes
Some groups entirely in Spanish:
No

Prerequisites

Calculus in several variaqbles and optimization. Mathematical Analysis

Objectives and Contextualisation

The applications of probability include practically all the sciences
and technology, being also the theoretical basis of Statistics. In
this course we will focus both on the theory (development of the
mathematical model of random phenomena) and on the most applied
aspects of modeling (find the right probability space) of real
problems and their resolution through the techniques learned.

Competences

  • Apply critical spirit and thoroughness to validate or reject both one’s own arguments and those of others.
  • Formulate hypotheses and devise strategies to confirm or reject them.
  • Identify the essential ideas of the demonstrations of certain basic theorems and know how to adapt them to obtain other results.
  • Recognise the presence of Mathematics in other disciplines.
  • Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
  • Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
  • Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
  • Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
  • Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
  • Take sex- or gender-based inequalities into consideration when operating within one's own area of knowledge.
  • Work in teams.

Learning Outcomes

  1. Apply critical spirit and thoroughness to validate or reject both one’s own arguments and those of others.
  2. Calculate probabilities in different spaces.
  3. Identify the main inequalities and discriminations in terms of sex/gender present in society.
  4. Recognise real situations in which the most common probabilistic distributions appear.
  5. Students must be capable of applying their knowledge to their work or vocation in a professional way and they should have building arguments and problem resolution skills within their area of study.
  6. Students must be capable of collecting and interpreting relevant data (usually within their area of study) in order to make statements that reflect social, scientific or ethical relevant issues.
  7. Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
  8. Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
  9. Students must have and understand knowledge of an area of study built on the basis of general secondary education, and while it relies on some advanced textbooks it also includes some aspects coming from the forefront of its field of study.
  10. Use random variables and know how to use them to model real phenomena.
  11. Use the concept of independence and apply central limit theorem to simple cases.
  12. Work in teams

Content

1.Probabilistic models

2. Random variables and vectors

3. Mathematical expectation

4. Convergence of sequences of random variables

5.Limit theorems of Probability Theory

Methodology

There will be three types of face-to-face activities: theory
classes, problem classes and practical classes. Attendance at the
practice sessions is mandatory.

This subject will use a Moodle Classroom in the UAB Virtual Campus:
http://cv.uab.cat. Students will be able to communicate with the
teachers through the email, always sent from the institutional
address @e-campus.uab.cat.

Activities

Title Hours ECTS Learning Outcomes
Type: Directed      
Classes of problems 30 1.2 1, 2, 9, 8, 6, 4, 11, 10
Classes of theory 30 1.2 1, 2, 9, 8, 6, 4, 11, 10
Type: Supervised      
Sessions of practice 6 0.24 1, 2, 9, 8, 6, 4, 11, 10
Type: Autonomous      
Personal study 118 4.72 1, 2, 9, 8, 6, 4, 11, 10

Assessment

Continued avaluation:

Assistance and delivery of four practices: 10% of weight.
Two partial (eliminatory) examinations, with a weight of 45% each.

Final examination of recuperation: of the two partial examinations  The marks of the partial examinatiosn can be improved.

Presented and not presented: Students who have presented at least 50% of the subject will be qualified as presented at the end of the course. Otherwise your rating will be Non-evaluable.



Assessment Activities

Title Weighting Hours ECTS Learning Outcomes
Continuous evaluation 100% 12 0.48 1, 2, 3, 9, 8, 7, 5, 6, 4, 12, 11, 10
Exam of recuperation 90% 4 0.16 1, 2, 3, 9, 8, 7, 5, 6, 4, 12, 11, 10

Bibliography

Bibliografy

Xavier Bardina. Càlcul de Probabilitats. Servei de Publicacions UAB,
2004.

Marta Sanz-Solé . Probabilitats. Edicions Universitat de Barcelona,
1999.

Aureli Alabert. Mesura i Probabilitat (2a ed.). Servei de
Publicaciones UAB, 1997. (Disponible a
http://gent.uab.cat/aureli_alabert/content/teaching)

Olga Julià, David Márquez, Carles Rovira i Mònica Sarrà.
Probabilitats: Problemes i més problemes. Publicacions i edicions
Universitat de Barcelona, 2005.