Elements of Probability and Statistics

Cod: 21037

Department: DCET

Department: DCET

ECTS: 6

Scientific area: Mathematics

Scientific area: Mathematics

Total working hours: 156

Total contact time: 26

Total contact time: 26

2. Probabilities

3. Discrete Random Variables

4. Continuous Random Variables

By completing this course the student should be able to:

- Translate into probability theory language problems related to uncertainty scenarios;
- Use concepts and rules of probability calculus in random variables;
- Apply in practical situations some of the most important distribution laws;
- Apply theoretical results for sums of random variables.

- Description of data and observations.

• Events and sets. Probability theory. Conditional probability.

• Unidimensional discrete and continuous random variables. Probability and Density functions. Distribution function. Moments of random variables.

• Discrete Distribution laws: discrete - uniform, Bernoulli, binomial, geometric, hypergeometric, Poisson.

- Continuous Distribution Laws: uniform, normal, exponential, gamma, chi-square. Sums of random variables.
- Central Limit Theorem and its corollaries.

• Relation between different random variables: covariance and correlation. Bivariate joint distributions.

F. Figueiredo, A. Figueiredo, A. Ramos, P. Teles, Estatística Descritiva e Probabilidades: Problemas Resolvidos e Propostos com Aplicações em R. 2ª Edição, Escolar Editora, 2009. ISBN 978-972-592-249-1

Complementary Reading (Optional):

J. Fonseca, Estatística Matemática, Vol I, Edições Sílabo. 2001. ISBN 972-618-243-3

Pedrosa, A. C., Gama, Sílvio Marques A., Introdução Computacional à Probabilidade e Estatística, Porto Editora, 2007.

E. Reis, P. Melo, R. Andrade, T. Calapez., Estatística Aplicada – Vol 1, Edições Sílabo, 2015

E-Learning.

This curricular unit requires competencies of Infinitesimal Analysis.