Course: 2024/2025

Probability I

(14458)

Requirements (Subjects that are assumed to be known)

The curriculum provides no prerequisite for courses. However, it is recommended that the students know the basic properties of real numbers, inequalities and are familiar with elementary functions, derivatives and integrals at a high school level.

Cognitive skills (knowledge): Summarize data information using basic graphical, tabular and numerical methods. Basic probability concepts. Conditional probability. Independence. Elementary calculus of probabilities. Discrete random variables. Probability mass functions. Continuous random variables. Probability distribution functions. Probability density functions. Calculus and interpretation of the expected value and variance of a given random variable. Binomial model, hypergeometric, geometric, Poisson, uniform, exponential, normal and gamma. Introduction to multivariate discrete random variables. Introduction to statistical software.
Transversal competences: Capacity development and model building and validation. Identification of relevant information to solve a problem. Visualization and interpretation solutions. Identification and location of logical errors. Logical argumentation in decision-making. Application of knowledge into practice.

Skills and learning outcomes

Description of contents: programme

1. Statistical description of data.
1.1. Variable types.
1.2. Frequency distributions.
1.3. Numerical measures to describe univariate data.
1.4. Graphical methods for data visualization.
2. Basic concepts of probability spaces.
2.1. Probability definition and properties.
2.2. Conditional probability and total probability rule.
2.3. Independence.
2.4. Bayes theorem.
2.5. Combinatorial notions and elementary calculus of probabilities.
3. One-dimensional discrete random variables.
3.1. Probability mass function, expected value and variance of discrete random variables.
3.2. Common discrete distribution models.
4. One-dimensional continuous random variables.
4.1. Probability density function, expected value and variance of continuous random variables.
4.2 Common continuous distribution models.
4.3. Distribution of transformations of random variables.
5. Multivariate discrete random variables
5.1 Definition and probability function
5.2 Independence of random variables
5.3 Mean and covariance matrix for multivariate random variables

Learning activities and methodology

Theory (4 ECTS). Theory classes with additional material available on the Web. Practical classes (2 ECTS) Problem solving classes. Problem-based learning classes.

Assessment System

- % end-of-term-examination 50
- % of continuous assessment (assigments, laboratory, practicals...) 50

Calendar of Continuous assessment

Extraordinary call: regulations

Basic Bibliography

- Dalgaard, Peter. Introductory statistics with R. Springer. 2008
- Durrett R.. Essentials of Probability. . Duxbury Press, Belmont CA. 1993
- Grimmett, G. y D. J. A. Welsh. . Probability: An introduction.. Oxford University Press. 2003
- Ugarte, María Dolores. Probability and statistics with R . CRC Press. 2008

The course syllabus may change due academic events or other reasons.