Subject: Statistics and Probability

Scientific Area:

Mathematics

80 Hours

Number of ECTS:

6 ECTS

Language:

Portuguese

# Overall objectives:

1 - As a basic course in Statistics and Probability, aims to enable the student to probability theory of knowledge that will be useful in understanding many technical situations that arise throughout the course and occupation.
2 - This course is also intended to go through the application of simple statistical techniques issues in business and administartion. Students will be able to use these statistical techniques to better analyze datasets, either through merely descriptive index calculation or by construction of confidence intervals, performing hypothesis testing to random variable parameters and building regression models.
3 - Students develop skills in understanding, with the essential critical thinking, data analysis and communication of results. This course is also intended to provide students with the capacity utilization and application of statistical software

# Syllabus:

1 - Descriptive Statistics and concentration indices
1 - Descriptive Statistics and concentration indices 1.1 - Population and sample; qualitative data and quantitative data. 1.2 - Location and scale measurements; shape measurements. 1.3 - Frequency distributions for grouped data. 1.4 - Graphical representation of data. 1.5 - Lorenz curve. 1.6 - Index based on Lorenz curve and Gini index.
1.1 - Population and sample; qualitative data and quantitative data.
1.2 - Location and scale measurements; shape measurements.
1.3 - Frequency distributions for grouped data.
1.4 - Graphical representation of data.
1.5 - Lorenz curve.
1.6 - Index based on Lorenz curve and Gini index.
2 - Index numbers.
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.
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 - 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.
3.1 - Random phenomena. Sample space.
3.2 - Kolmogoroff's axiomatic.
3.3 - Conditional probability. Total probability theorem. Bayes' Theorem.
4 - Random variables.
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.
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 - 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.
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 - 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.
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:

Mendenhall W., Sincich T. , 2003 , A Second Course in Statistics: Regression Analysis , Prentice & Hall
Aczel, A. D. , 1995 , Statistics - Concepts and Applications , Irwin
Pestana, D., Velosa, S. , 2010 , Introdução à Probabilidade e à Estatística, Vol. I, 4ª edição , Fundação Calouste Gulbenkian
Hoaglin, D., Mosteller, F., Tukey, J. , 1992 , Análise Exploratória de Dados, Técnicas Robustas , Edições Salamandra
Galvão de Mello, F. , 2000 , Probabilidades e Estatística, Conceitos e Métodos Fundamentais , Escolar Editora
Murteira, B. J. F. , 1990 , Probabilidades e Estatística, vol. I e II, 2ª ed , McGraw-Hill
A. Afonso, C. Nunes , 2011 , Estatística e Probabilidades - Aplicações e Soluções em SPSS , Escolar Editora
D. Waller , 2008 , Statistics for Business , Elsevier
M. F. Triola, L. A. Franklin , 1994 , Business Statistics - Understanding Populations and Processes , Addison- Wesley

# 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%.