Probability and Statistics

Objectives

In this curricular unit an introduction to the basic concepts and methodologies of Probability Theory and Statistical Inference, the latter in its parametric version. The students should be capable of doing an exploratory data-analysis, apply correctly the probabilistic models studied and perform a statistical analysis, especially when normal populations are involved. They should also be capable of adjusting a simple linear regression model and test the significance of the model’s parameters.

Program

1. Exploratory Data-Analysis.
2. Fundamental Concepts of Probability.
3. Random Variables and Random Vectors.
4. Discrete and Continuous Probability Distributions.
5. Random Sampling.
6. Point Estimation.
7. Confidence Estimation.
8. Testing of Hypothesis.
9. An Introduction to Simple Linear Regression.

Teaching Methodologies

The theory classes will have an expository component, always accompanied by some application examples. The teacher/student interaction will also be an important component in both theory and practice classes. In the latter, the student will have a first contact with a statistical package,which will be used to perform statistical analyses throughout the semester. The students grades will be the result of her/his performance in two written tests.

Bibliography

- Guimarães, R.C. e Cabral, J.A.S. (1997). Estatística. McGraw-Hill, Lisboa.
- Montgomery e Runger (2003). Applied Statistics and Probability for Engineers, Wiley, New York.
- Murteira, B., Ribeiro, C., Silva, J. e Pimenta, C. (2002). Introdução à Estatística, McGraw-Hill, Lisboa.
- Pestana, D.D. e Velosa, S.F. (2006). Introdução à Probabilidade e Estatística, Vol. I., 2ª ed., Fundação Calouste Gulbenkian, Lisboa.