Probability and Statistics

Code	12924
Year	2
Semester	S1
ECTS Credits	6
Workload	TP(60H)
Scientific area	Mathematics
Entry requirements	None.
Learning outcomes	Students are expected to be able to obtain a sample to carry out a project, to describe the sample data and summarize the information. Students are also expected to solve problems using introductory topics of Theory of Probability, and inferential methods concerning confidence intervals and parametric hypothesis tests. The SPSS statistical program will be used.
Syllabus	DESCRIPTIVE STATISTICS Data collection. Introduction to SPSS. Frequency tables of one-dimensional and two-dimensional variables. Graphical representations of one-dimensional and two-dimensional variables. Numerical characteristics of a distribution. Linear relationship between two variables. PROBABILITY THEORY Random Experiments. Results space. Events. Axiomatic definition of probability. Properties. Laplace's law. Conditioned probability. Independence. Total Probability Theorem and Bayes Theorem. Random variables (discrete and continuous). Distribution function. Probability function. Probability density function. Expected value of a random variable. Variance and standard deviation of a random variable. Theoretical distributions. STATISTICAL INFERENCE Sampling methods. Sample distribution of the mean. Confidence Intervals. Introduction to hypothesis testing. Validation of parametric test assumptions. Some parametric hypothesis tests.
Main Bibliography	Murteira, B., Ribeiro, C., Silva, J. e Pimenta, C. (2015), Introdução à Estatística – 3ª edição. Escolar Editora. Maroco, João (2018). Análise Estatística com a utilização do SPSS, 7ª edição, Ed. Report Number. Guimarães, R. C. e Sarsfield Cabral, J. A. (2010), Estatística – 2ª edição. Editora Verlag Dashofer.
Language	Portuguese. Tutorial support is available in English.