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# Probability and Statistics D

2085

### Department

Departamento de Matemática

5.0

### Teacher in charge

Isabel Cristina Maciel Natário, João Tiago Praça Nunes Mexia

4

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 primitives, integrals and functions of more than one variable.

### Subject matter

Short syllabus

1. Descriptive Statistics

2. Basic notions of probability.

3. Random variables and their probability distributions.

4. Moments of random variables.

5. Some important distributions.

6. Random vectors.

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 (2005). 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. Also lab classes using the statistical software R to solve problems.

### Evaluation method

Evaluation Rules

The evaluation in this subject comprises a written examination plus a (computational) practical test.

The written examination must be one of two: either the students take 2 tests or one exam. Each test covers half of the subjects taught. Students must be classified over 8/20 in both tests or in the exam.

The practical test is done during the last laboratorial class.

The final grade is a weighted average of the written examination grade plus the computational work grade.