Subject: Statistics and Probability

Scientific Area:

Mathematics

80 Hours

Number of ECTS:

6 ECTS

Language:

Portuguese

Overall objectives:

1 - Since it is a first graduate course of Probability and Statistics, the students are expected to acquire theoretical and practical knowledge of statistics and probability that will be useful in understanding technical issues in other curricular units of their degree and in their professional activity.
2 - This curricular unit covers the application of simple statistical techniques to a range of problems in economics. Students will be able to use these statistical techniques to improve data analysis when they are determining descriptive indexes, confidence intervals, performing hypothesis tests to parameters of random variables, or applying regression models.
3 - Students will develop skills in understanding data analysis and reporting results. This course is also intended to provide students with skills to apply and use statistical softwares (SPSS or R, for example) in statistical analysis.

Syllabus:

1. - Concentration indexes
1.1 - Lorenz curve.
1.2 - Index based on Lorenz curve and Gini index.
2. - Index numbers.
2.1 - Simple indexes and synthetic indexes.
2.2 - The Laspeyre and the Paasche indexes.
2.3 - Fisher's ideal index.
2.4 - Other definitions and properties.
3 - Basic concepts of Probability Theory.
3.1 - Random phenomena. Sample space.
3.2 - Kolmogoroff's axiomatic.
3.3 - Conditional probability. Total probability theorem. Bayes' Theorem.
4. - Random variables.
4.1 - Definition of random variable. Discrete random variables and continuous random variables.
4.2 - Distribution function of a random variable.
4.3 - Probability distribution and density function.
4.4 - Moments of a random variable.
4.5 - Some discrete random variables: binomial;hipergeometric;geometric;negative binomial;Poisson.
4.6 - Some continuous random variables: normal, chi-squared, t, F.
4.7 - Random vectors. Joint probability distribution. Marginal distributions. Conditional distributions.
4.8 - Covariance. Independent random variables.
4.9 - The sum of random variables.
4.10 - Central Limit Theorem.
5. - Statistical Inference.
5.1 - Random samples. Simple random sample and stratified random sample.
5.2 - Estimator and estimate.
5.3 - Confidence intervals.
5.4 - The estimation error and the random sample dimension.
5.5 - Statistical hypothesis tests.
6. - Simple linear regression.
6.1 - The simple linear regression model. The correlation coefficient.
6.2 - Estimation.
6.3 - The model fit. Residuals analysis. Outliers and influence diagnosis.

Literature/Sources:

M. Barrow , 2009 , Statistics for Economics, Accouting and Business Studies , Prentice Hall
F. Figueiredo, A. Figueiredo, A. Ramos, P. Teles , 2009 , Estatística Descritiva e Probabilidades - Problemas resolvidos e propostos com aplicações em R , Escolar Editora
B. J. F. Murteira, M. Antunes , 2012 , Probabilidades e Estatística , Escolar Editora
A. D. Aczel , 2005 , Statistics - Concepts and Applications , Irwin
B. J. F. Murteira, C. S. Ribeiro, J. Andrade e Silva, C. Pimenta, F. Pimenta , 2015 , Introdução à Estatística , Escolar Editora
M. F. Triola, L. A. Franklin , 1994 , Business Statistics - Understanding Populations and Processes , Addison- Wesley
A. Afonso, C. Nunes , 2011 , Estatística e Probabilidades - Aplicações e Soluções em SPSS , Escolar Editora
D. D. Pestana, S. F. Velosa , 2008 , Introdução à Probabilidade e à Estatística , Fundação Calouste Gulbenkian
D. Waller , 2008 , Statistics for Business , Elsevier
M. Barroso, E. Sampaio, M. Ramos , 2010 , Exercícios de Estatística Descritiva para as Ciências Sociais , Edições Sílabo

Assesssment methods and criteria:

Classification Type: Quantitativa (0-20)

Evaluation Methodology:
Teaching Methodologies: Lectures. Solving exercises and problems with a statistical software or a calculator. Obtaining statistical analysis and interpreting the outputs. Evaluation: Two mandatory tests each weighting 50%.