Probability and Stochastic Processes
Code: 107844 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| Electronic Engineering for Telecommunications | FB | 1 |
| Telecommunication Systems Engineering | FB | 1 |
Contact
- Name:
- Armengol Gasull Embid
- Email:
- armengol.gasull@uab.cat
Teachers
- David Rojas Perez
- Salim Boukfal Lazaar
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
Differential and integral calculus.
Objectives and Contextualisation
To familiarize the student with the techniques and methods of probabilistic modeling using random variables and stochastic processes. To develop the ability to apply these techniques in the resolution of practical problems, common in the engineering profession, for which a probabilistic mathematical model can provide a more appropriate solution than a deterministic model.
Learning Outcomes
- KM02 (Knowledge) Interpret random phenomena using probability theory and statistics
- KM02 (Knowledge) Interpret random phenomena using probability theory and statistics
- SM02 (Skill) Evaluate probabilities in random events in telecommunications engineering.
- SM02 (Skill) Evaluate probabilities in random events in telecommunications engineering.
- SM03 (Skill) Evaluate statistical parameters of variables and processes in telecommunications engineering.
- SM03 (Skill) Evaluate statistical parameters of variables and processes in telecommunications engineering.
- SM04 (Skill) Express oneself appropriately using the basic mathematical language in telecommunications engineering.
- SM04 (Skill) Express themselves appropriately using basic mathematical language in telecommunications engineering.
Content
1. Probability
- Randomness, probability spaces and Kolmogorov's axioms
- Combinatorics
- Independence and conditional probability
- Total probability formula and Bayes' formula.
2. Discrete random variables
- Probability and distribution functions
- Expectation, variance and standard deviation
- Binomial, geometric, Poisson and other distributions
3. Continuous random variables
- Density and distribution functions
- Expectation, variance and standard deviation
- Chebyshev's inequality
- Exponential, uniform, normal and other distributions
4. Convergence of sequences of random variables
- Law of large numbers
- Central limit theorem. Approximations to the normal.
5. Random vectors
- Joint and marginal distribution of two or more random variables
- Conditional distributions. Independence
- Conditional expectation, covariance and correlation coefficient
- Bivariate and multivariate normal distribution
6. Stochastic processes
- Basic definitions: trajectories and finite-dimensional distributions
- Strictly stationary (SS) and weakly stationary (WS) processes
- Cyclo-stationary processes
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Problem classes | 12 | 0.48 | KM02, KM02, SM02, SM03, SM04 |
| Theory classes | 36 | 1.44 | KM02, KM02, SM02, SM03, SM04 |
| Type: Autonomous | |||
| Student's individual work | 94 | 3.76 | KM02, KM02, SM02, SM03, SM04 |
The subject has three hours of theory per week. They will be taught in the traditional way with a blackboard. In these classes, the main ideas on the various topics will be given, showing examples and applications. The student will receive lists of exercises and problems that will be worked on in the weekly problem class. Previously, during their non-face-to-face activity, they will have to read and think about the proposed exercises and problems.
The UAB virtual campus will be used regularly to communicate with students and to share useful materials for the course.
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
Continous Assessment Activities
| Title | Weighting | Hours | ECTS | Learning Outcomes |
|---|---|---|---|---|
| Problems evaluation-1 | 10% | 1 | 0.04 | KM02, SM02, SM03, SM04 |
| Problems evaluation-2 | 10% | 1 | 0.04 | KM02, SM02, SM03, SM04 |
| Test 1 | 40% | 3 | 0.12 | KM02, SM02, SM03, SM04 |
| Test 2 | 40% | 3 | 0.12 | KM02, SM02, SM03, SM04 |
There will be four grades (over 10) to evaluate the course continuously:
- Partial Exam 1 (EP1) and Partial Exam 2 (EP2). Problems similar to those worked on during the problem classes and some theoretical questions will have to be solved.
- Problem Assessment 1 (AP1) and Problem Assessment 1 (AP2). Multiple-choice exams on basic content worked on in the subject.
The course grade (Q) will be obtained using the formula,
Q = 0.4 EP1+0.4 EP2+0.1 AP1+0.1 AP2
Students who obtain Q>=5 will have passed the subject and will have this course grade.
For students who do not pass, there will be a single retake exam that will be on the entire course subject, with a grade of Q2, over 10, which will replace the four continuous assessment tests. To pass the subject, Q2 must be greater than or equal to 5.
Bibliography
BASICS:
Software
No specific software will be used.
Groups and Languages
Please note that this information is provisional until 30 November 2025. You can check it through this link. To consult the language you will need to enter the CODE of the subject.
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 311 | Catalan/Spanish | second semester | morning-mixed |
| (PAUL) Classroom practices | 312 | Catalan/Spanish | second semester | morning-mixed |
| (PAUL) Classroom practices | 331 | Catalan/Spanish | second semester | morning-mixed |
| (PAUL) Classroom practices | 332 | Catalan/Spanish | second semester | morning-mixed |
| (TE) Theory | 31 | Catalan/Spanish | second semester | morning-mixed |
| (TE) Theory | 33 | Catalan/Spanish | second semester | morning-mixed |