3

2018-2019

01001286

Mathematics

Portuguese

Face-to-face

SEMESTRIAL

6.0

Compulsory

1st Cycle Studies

Probability.

Classes are expository and include examples and exercises for applying the acquired knowledge. Analysis of real or simulated data using the statistical software SPSS will be developed in laboratorial classes. Throughout the semester, students may develop and present studies on statistical applications.

During the semester, students can also use tutorial time to discuss their ideas and clarify possible understanding difficulties.

Statistical goal is the study and description of random phenomena by estimating the probability distribution underlying such phenomena. The Descriptive Statistics, which includes the Exploratory Data Analysis, resumes and draws the main conclusions about the recorded data. In the Mathematical Statistics, supported on Probability, inferential methods are developed to evaluate the quality of the statistical conclusions about the general phenomena under study. To better reach these goals, this course is complemented with the analysis of real and simulated data using a statistical package (SPSS).

This course allows developing the following skills: ability to calculate; using computational tools; knowledge of mathematical results; ability to generalize and abstract; design and use of mathematical models for real situations. On a personal level, it allows to develop individual initiative, teamwork, research and independent learning.

Introduction - Descriptive Statistics and Mathematical Statistics. I – Descriptive Statistics: Exploratory Data Analysis. Univariate and multivariate statistical variables. Association and regression. II – Introduction to Mathematical Statistics: Sampling and statistical models. Statistics. III – Parametric Estimation: A/ Point estimation: unbiased and consistent estimators. Estimation methods: method of moments; maximum likelihood method. B/ Interval estimation: pivotal–quantity method. Sampling from the normal distribution. Large-sample confidence intervals. IV – Tests of Hypotheses and Applications. Critical region and types of errors; size, power and p-value. Neyman-Pearson tests. Chi-square goodness-of-fit tests. Simple linear model: Minimum square estimators. Gaussian case: inference on model parameters and prediction.

Maria de Nazaré Simões Quadros Mendes Lopes

Assessment

*Exam (100%) or Midterm exam (70%) + Test (30%): 100.0%*

E. Gonçalves and N. Mendes-Lopes, Estatística -Teoria Matemática e Aplicações, Escolar Editora, 2003.

E. Gonçalves, N. Mendes-Lopes, Probabilidades - Princípios Teóricos, 2ªed., Escolar Editora, 2013.

A. Mood, F. Graybill and D. Boes, Introduction to the theory of Statistics. 3th edition, MCGraw-Hill International Editions, 1974.

D. Moore and G. McCabe, Introduction to the practice of Statistics. 4th edition, Freeman, 2003.

D. Pestana and S. Velosa, Introdução à Probabilidade e à Estatística, Vol. I, 2ª ed., Fundação Calouste Gulbenkien, 2006.

V.K. Rohatgi, An introduction to Probability Theory and Mathematical Statistics, John Wiley & Sons Inc., 1976.

Ph. Tassi, Méthodes Statistiques, Éditions Technip, 1992