Universidade Nova de Lisboa

Universidade Nova de Lisboa

Faculdade de Ciências e Tecnologia

Probability and Statistics D

Code

10354

Academic unit

Faculdade de Ciências e Tecnologia

Department

Departamento de Matemática

Credits

6.0

Teacher in charge

Isabel Cristina Maciel Natário

Weekly hours

4

Total hours

56

Teaching language

Português

Objectives

It is objective of this subject to teach the basics about the theory of probability, namely about probability, conditional probability, independence, random variables - their distribution, moments and some other characteristics - and the central limit theorem.

 

The above matters are then used to teach the fundamentals about statistics, as the notion of population, sample and random sample, estimators, their sample distributions and some other properties, point estimation, estimation by confidence interval, hypotheses testing and simple linear regression.

 

The key important point here is one of teaching these subjects in a way that, in the future, students can use adequately these statistical tools and can easily learn other statistical methods, that could not have been included in here.

 

Prerequisites

Basics of mathematical analysis, pointing out some topological notions, primitives, integrals and functions of more than one variable.

Subject matter

Short syllabus

 1. Descriptive Statistics 

2. Basic notions of probability 

3. Discrete random variables, their probability distributions and moments 

4. Discrete random vectors 

5. Continuous random variables, their probability distributions and moments

6. Some important distributions  

7. Central limit theorem 

8. Basic notions of statistics 

9. Point and interval estimation 

10. Hypothesis testing 

11. Simple linear regression

 

Bibliography

Guimarães e Cabral (1997). Estatística. McGraw-Hill.

Kvanli (1988). Statistics. West Publishing Company.

Montgomery e Runger (2002). Applied Statistics and Probability for Engineers. Wiley.

Mood, Graybill e Boes (1974). Introduction to the Theory of Statistics. McGraw-Hill.

Natário (2010). Notas de apoio à disciplina de Probabilidade e Estatística D. DMAT.

Paulino e Branco (2005). Exercícios de Probabilidade e Estatística. Escolar Editora.

Rohatgi (1976). An Introduction to Probability Theory and Mathematical Statistics. Wiley.

Sokal e Rohlf (1995). Biometry. Freeman.

Tiago de Oliveira (1990). Probabilidades e Estatística: Conceitos, Métodos e Aplicações, vol. I, II. McGraw-Hill.

Teaching method

Lectures and problem-solving sessions, with wide participation of students. 

Evaluation method

There are three tests that can substitute the final exam in case of approval. Otherwise the student must take the final exam. More detailed rules are available in the Portuguese version.

 

 

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