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Probability and Stochastic Modelling

Code: 100104
Credits: 8
2026/2027
Degree programme Type Course
Mathematics OB 3

Contact lecturer

Name :
Francisco Javier Delgado Vences
Email :
franciscojavier.delgado@uab.cat

Teaching staff

Giulia Binotto
Ramon Gallardo Campos
Aureli Alabert Romero

Group languages

You can consult this information at the end of the document.

Prerequisites

Calculus in different variables and optimization.
Mathematical analysis.

Objectives

The theory of probability has its origins in the 17th century with the first formalizations of the notion of chance motivated by issues related to games. Its applications cover practically all sciences and technologies and constitute the theoretical basis of Statistics.
In this subject, we will focus both on the theory (development of the mathematical model of random phenomena) and on some more applied aspects of modeling real problems and their resolution using the techniques learned.

Learning outcomes

  1. 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.
  2. 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.
  3. 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.
  4. Students must be capable of communicating information, ideas, problems and solutions to both specialised and non-specialised audiences.
  5. Students must develop the necessary learning skills to undertake further training with a high degree of autonomy.
  6. Apply critical spirit and thoroughness to validate or reject both one's own arguments and those of others.
  7. Work in teams
  8. Recognise real situations in which the most common probabilistic distributions appear.
  9. Use the concept of independence and apply central limit theorem to simple cases.
  10. Use random variables and know how to use them to model real phenomena.
  11. Calculate probabilities in different spaces.
  12. Identify the main inequalities and discriminations in terms of sex/gender present in society.

Contents

1. Probabilistic models


2. Random variables and vectors


3. Mathematical expectation


4. Convergence of random variables


5. Laws of large numbers


6. Central limit theorem

Learning activities and methodology

Title Hours ECTS Learning outcomes
Classes of theory 30 1.2 1, 3, 5, 6, 8, 9, 10, 11
Personal study 118 4.72 1, 3, 5, 6, 8, 9, 10, 11
Classes of problems 28 1.12 1, 3, 5, 6, 8, 9, 10, 11
Sessions of practice 8 0.32 1, 3, 5, 6, 8, 9, 10, 11

There will be three types of face-to-face activities: theory classes, problem classes and practical classes.

For this course, the use of AI technologies is permitted exclusively for support tasks, such as bibliographic or information searches, text correction, and translations. Students must clearly indicate which parts have been generated using this technology, specify the tools used, and include a critical reflection on how these tools have influenced both the process and the final outcome of the activity. Failure to be transparent about the use of AI in this assessed activity will be considered academic dishonesty and may result in a partial or total penalty on the activity's grade, or more serious sanctions in severe cases.

Annotation: within the schedule set by the centre or degree programme, 15 minutes of one class will be reserved for students to evaluate their lecturers and their courses or modules through questionnaires.

Assessment

Continuous assessment activities

Title Weight Hours ECTS Learning outcomes
Final exam 45% 2 0.08 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12
Exam of recuperation 90% 2 0.08 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12
Midterm exam 45% 2 0.08 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12
Continuous evaluation 20% 10 0.4 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12

Continuous assessment:

  • Practical exam: 10% of the grade.
  • Two midterm exams, each worth 45%.

Single assessment:

On the day scheduled for the second midterm exam: assessment or submission of the four practical assignments (10%) and completion of two exams (45% each), covering the first and second parts of the course, respectively.

To pass the course, a minimum of 3.5 (out of 10) is required in each exam and in the practical component.

Please contact the instructors as soon as possible to clarify details.

Resit exam: This will count for 90% and may be used to improve the grade of each midterm. Attending the resit implies forfeiting the previously obtained grade.

Minimum grade: To pass the course, a minimum of 4 is required in each midterm (or its resit) and a minimum overall average of 5.0. Grades that do not meet these requirements may be reviewed on a case-by-case basis.

Honors: For the possible awarding of Honors, resit grades will not be taken into account.

Attended / Not attended: Students who have completed at least 50% of the course content will be recorded as attended at the end of the course. Otherwise, their status will be Not Assessed.


Bibliography

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

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

Quentin Berger, Francesco Caravenna, Paolo Dai Pra. Probabilità. Un primo corso attraverso esempi, modelli e applicazioni. UNITEXT, volume 127, Springer, 2021. 

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.

 

Software

In practical classes, we will make use of the R programming language and the Rstudio environment.

Course groups and languages

The information provided is provisional until November 30. After this date, you will be able to consult the language of each group through this link. To access the information, you will need to enter the course CODE

Type of teaching Group Language Semester Shift
(TE) Theory 1 Catalan/Spanish first semester morning-mixed
(PAUL) Classroom practices 1 Catalan first semester morning-mixed
(PLAB) Practical laboratories 1 Spanish first semester morning-mixed
(PAUL) Classroom practices 2 Catalan first semester morning-mixed
(PLAB) Practical laboratories 2 Spanish first semester morning-mixed