Base Knowledge
Recommended Knowledge
Fundamental notions of set algebra, differential and integral calculus.
Teaching Methodologies
The content is developed through an approach focused on conceptual understanding and the practical application of Probability and Statistics in engineering contexts, combining structured exposition with guided exploration of exercises and problems. Learning is complemented by mathematical tasks designed to promote critical thinking, result validation, and the identification of limitations, encouraging students to reflect on ethical implications in data analysis and interpretation. Task-solving aims to stimulate discussion, collaborative construction of solutions, and the development of communication skills essential for future professional practice. To carry out these tasks, students will use digital tools, including artificial intelligence systems, not only to represent and compute, but also to critically analyse data, consolidate concepts, build new knowledge, and communicate it clearly and with sound justification.
Learning Results
To provide the foundations of Statistics required for the analysis and interpretation of data in the health sciences, presenting probability models with applications in the fields of engineering.
To develop the ability to think and reason statistically, to interpret results rigorously and to exercise critical thinking, by understanding the principles that support the modelling of random phenomena and quantitative analysis in biomedical contexts.
To learn essential methods of data analysis and to understand the probabilistic models that underpin statistical inference, applying confidence intervals and hypothesis tests.
To master simple linear regression, integrating representation, interpretation and computation, and to use artificial intelligence tools appropriately and responsibly in the study of problems with real-world applicability.
Program
Syllabus
1. Introduction
1.1. Descriptive statistics and inferential statistics
1.2. Population and sample
2. Probability
2.1. Fundamental concepts
2.2. Random experiment, space of outcomes and events
2.3. Notion of Probability
2.4. Conditional probability and independence
3. Random variables and main theoretical distributions
3.1. Discrete Random Variables and Continuous Random Variables
3.2. Location and dispersion parameters
3.3. Discrete special distributions:
3.3.1. Hypergeometric
3.3.2. Binomial
3.3.3. Poison
3.4. Continuous special distributions:
3.4.1. Uniform
3.4.2. Exponential
3.4.3. Normal
4. Sampling
4.1. Sampling distributions
5. Introduction to statistical inference
5.1. Point estimation and Interval estimation
5.2. Confidence intervals and hypothesis tests for population parameters
6. Linear regression
6.1. Scatter diagram, correlation and linear regression
6.2. Simple linear regression model
6.3. Confidence intervals and tests in regression
Curricular Unit Teachers
Corália Maria Santos PimentaGrading Methods
- Each task is worth 2 marks, giving a total of 6 marks. The tasks cover the topics taught in the course, namely probability and events, discrete and continuous probability distributions, estimation, and hypothesis testing. Tasks may be completed individually or in pairs and must be presented in a formal and rigorous manner. Task assessment will take into account the scientific and methodological quality of the work, valuing students’ ability to independently and critically apply relevant knowledge in order to develop a well-founded critical analysis of the solutions generated by the Artificial Intelligence tool used. Particular attention will also be given to the rigour of result validation, the identification of errors or limitations, the precision of the mathematical language used, and the clarity and correctness of the reasoning presented.
- The written tests are individual, last two hours, and do not allow the use of any reference materials. Each test is worth 7 marks, giving a total of 14 marks. The first test covers probability, random variables, and discrete distributions. The second test covers random variables, continuous distributions, sampling, estimation, and hypothesis testing. A minimum mark of 3.50 is required in each test.
- Marks obtained in individual assessment components are not rounded; only the final mark may be rounded.
- If a student achieves the minimum mark in the first test but does not obtain a final mark of at least 9.50, they may retake only the second test in any examination period. Students who do not pass through continuous or periodic assessment, or who choose not to undertake this form of assessment, may sit the final examination, which is worth 20 marks. A mark of at least 9.50 is required to pass.
Internship(s)
NAO
Bibliography
Bibliography
Recommended:
Notes for theoretical classes, provided by the teacher (Moodle / Inforestudante).
Figueiredo, F., et al. (2009). Estatística descritiva e probabilidades: Problemas resolvidos e propostos com aplicações em R (2.ª ed.). Escolar Editora.
Guimarães, R. C., & Cabral, J. A. S. (2007). Estatística (2.ª ed.). McGraw-Hill.
Montgomery, D. C., & Runger, G. C. (2018). Applied statistics and probability for engineers. Wiley.
Pedrosa, A. C., & Gama, S. M. A. (2018). Introdução computacional à probabilidade e estatística. Porto Editora.
Complementary:
Bowker, A., & Lieberman, G. (1972). Engineering statistics (2.ª ed.). Prentice Hall.
Murteira, B., et al. (2002). Introdução à estatística. McGraw-Hill.
Nunes, C. (2012). Probabilidades e estatística: 275 problemas resolvidos (utilização do R). Escolar Editora.
Ross, S. M. (2004). Introduction to probability and statistics for engineers and scientists (3.ª ed.). Elsevier.