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

In this curricular unit, the basic concepts of probability and statistical theory are introduced. Starting with a reference to some of the methods of description of the data and observations, it continues with the concept of uncertainty associated with the events and the most fundamental concepts of probability theory. Random variables are introduced, the notions of discrete and continuous random variables, and some of the most important distribution laws and theoretical results.

1. Descriptive statistics

2. Probabilities

3. Discrete Random Variables

4. Continuous Random Variables

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.

• 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.

Compulsory Reading:

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

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.

Continuous assessment is privileged: 2 or 3 digital written documents (e-folios) during the semester (40%) and a
presence-based final exam (p-folio) in the end of the semester (60%). In due time, students can alternatively choose to perform one
final presence-based exam (100%).