Probability and Statistics E
Code
9414
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Frederico Almeida Gião Gonçalves Caeiro
Weekly hours
4
Total hours
71
Teaching language
Português
Objectives
It is objective of this subject to teach the basics about probability theory, namely about probability, conditional probability, independence, random variables - their distribution, moments and some other characteristics - and the central limit theorem.
Learn the fundamentals about statistics, as the notion of population, sample and random sample, estimators, their sample distributions and some other properties, point estimation, estimation by confidence interval, hypotheses testing and simple linear regression.
Prerequisites
Basics of mathematical analysis, pointing out some topological notions, primitives, integrals and functions of more than one variable.
Subject matter
1. Basic notions of probability.
2. Random variables and their probability distribution.
3. Moments of random variables.
4. Some important distributions.
5. Random vectors.
6. Central Limit Theorem.
7. Random number generation.
8. Point estimation.
9. Interval estimation.
10. Hypothesis testing.
11. Simple linear regression.
Bibliography
Guimarães e Cabral (1997). Estatística. McGraw-Hill.
Montgomery e Runger (2002). Applied Statistics and Probability for Engineers. Wiley.
Mood, Graybill e Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.
Murteira, B., Ribeiro, C., Silva, J. e Pimenta, C. (2007). Introdução à Estatística, 2ª edição. McGraw-Hill
Paulino e Branco (2005). Exercícios de Probabilidade e Estatística. Escolar Editora.
Pestana, D. e Velosa, S. (2002). Introdução à Probabilidade e à Estatística. Fundação Calouste Gulbenkian, Lisboa.
Rohatgi (1976). An Introduction to Probability Theory and Mathematical Statistics. Wiley.
Sokal e Rohlf (1995). Biometry. Freeman.
Tiago de Oliveira (1990). Probabilidades e Estatística: Conceitos, Métodos e Aplicações, vol. I, II. McGraw-Hill.
Teaching method
Lectures and problem-solving sessions, with wide participation of students.
Evaluation method
There are two tests that can substitute the final exam in case of approval. Otherwise the student must do the final exam. More detailed rules are available in the Portuguese version.