Probability
Code: 104847 ECTS Credits: 6| Degree | Type | Year |
|---|---|---|
| 2503852 Applied Statistics | FB | 1 |
Contact
- Name:
- Maria Merce Farre Cervello
- Email:
- merce.farre@uab.cat
Teaching groups languages
You can view this information at the end of this document.
Prerequisites
Calculus 1 and Introduction to Probability.
Objectives and Contextualisation
Probability is a branch of Mathematics that has multiple applications in practically all areas of science and technology.
It is also the language of inferential statistics. By this reason, this is one of the fundamental subjects of the Degree in Applied Statistics.
In this second course, it is intended to deepen in some of the subjects started in the Introduction to Probability course and to present new topics
such as simulation of random variables and Markov chains.
Learning Outcomes
- KM10 (Knowledge) Describe the characteristics of the distribution and density functions of random variables.
- SM09 (Skill) Analyse data through different inference techniques using statistical software.
Content
1. Generating random variables based on uniform random numbers.
2. Random vectors:
- Expectation of a function of a random vector. Covariance and correlation.
- Independent random variables.
- Conditional expectation.
- Computations in the discrete case.
3. The moments of a random variable and the moments' generating function. Properties and applications.
4. Convergence of a sequence of random variables: almost-sure, in probability and in distribution. Relations and properties.
5. The Laws of Large Numbers and de Central Limit Theorem. Applications.
6. Introduction to random processes: Random Markov Chains with a finit number of states. The probabilities' generating function.
Activities and Methodology
| Title | Hours | ECTS | Learning Outcomes |
|---|---|---|---|
| Type: Directed | |||
| Classes of problems | 18 | 0.72 | |
| Classes of theory | 26 | 1.04 | |
| Type: Supervised | |||
| Classes of practice | 8 | 0.32 | |
| Type: Autonomous | |||
| Personal study | 82 | 3.28 |
There will be three types of face-to-face activities: theory classes, problem classes and practical classes. In theory classes the concepts and results that form the heart of the subject will be developed. A collection of problem lists will be edited for class work of problems that students should have worked on before. The practices will be in the computer rooms and specialized software will be used, such as R. Attendance to the practical classes is mandatory.
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 |
|---|---|---|---|---|
| Continued evaluation | 100% | 12 | 0.48 | KM10, SM09 |
| Exam of recuperation | 80% | 4 | 0.16 | KM10, SM09 |
The continuous assessment will consist of two partial exams (theory and problems) with a respective weight of 35% the first (P1) and 45% the second (P2), and the assessment of classroom or computer-based practices (Pr) which will represent 20% of the final mark.
NF = 0.35·P1 + 0.45·P2 + 0.2·Pr
In the evaluation of the practices, the delivery of scheduled tasks and the completion of controls will be taken into account.
The recoverable part of the final exam will only be the one corresponding to the partial exams. The partial exams are eliminatory.
To pass the subject you need to have a minimum of 3.5 in the weighted average of the partials (or the recovery) and in the average grade of the practical part, in addition to a minimum of 5 in NF.
Single evaluation
The single evaluation will be a test of synthesis of the competences of both partials, based on: (1) An exam with theory questions and problems (weight: 80%). (2) A practice test in front of the computer (weight: 10%). (3) The delivery of scheduled tasks that are indicated, with the possibility that the faculty ask the student to explain details of these deliveries (weight: 10%).
Bibliography
X. Bardina. Càlcul de probabilitats. Materials UAB, 139.
M.H. de Groot. Probabilidad y estadística. Addison-Wesley Iberoamericana.
W. Mendenhall et al. Estadísitica Matemática con aplicaciones. Grupo editorial Iberoamérica.
K.L. chung. Teoría elemental de la probabilidad y los procesos estocásticos. Ed. Reverté.
S.M. Ross. A First course in probability. Ed. MacMillan.
Software
We will use statistical software R.
Language list
| Name | Group | Language | Semester | Turn |
|---|---|---|---|---|
| (PAUL) Classroom practices | 1 | Catalan | second semester | morning-mixed |
| (PLAB) Practical laboratories | 1 | Catalan | second semester | afternoon |
| (PLAB) Practical laboratories | 2 | Catalan | second semester | afternoon |
| (TE) Theory | 1 | Catalan | second semester | afternoon |