# Probability and Statistics E

## Objectives

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

Learn 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, simple linear regression and rudiments in stochastic simulation.

## General characterization

##### Code

9414

##### Credits

6.0

##### Responsible teacher

Filipe José Gonçalves Pereira Marques, Maria de Fátima Varregoso Miguens

##### Hours

Weekly - 4

Total - 65

##### Teaching language

Português

### Prerequisites

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

### Bibliography

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

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

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

Murteira, B., Ribeiro, C., Silva, J. e Pimenta, C. (2007). Introdução à Estatística, 2ª edição. McGraw-Hill

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

Pestana, D. e Velosa, S. (2002). Introdução à Probabilidade e à Estatística. Fundação Calouste Gulbenkian, Lisboa.

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

**Frequency note:**

In all classes will be marked the presence of the students. Frequency will be attributed to students who do not lack, unjustifiably, more than 8 (eight) classes corresponding to the shift in which they are enrolled. This rule is valid for all students, with the exception of:

- students with the status of student worker, or any other recognized by the faculty evaluation rules;

- students who attended the previous school year classes.

Continuous evaluation

Continuous evaluation consists of three tests. The three tests will have a T1, T2 and T3 rating classified on a scale of 0 to 20 values. The final classification of the continuous evaluation is calculated through

Final classification = 0.4 T1 + 0.4 T2 + 0.2 T3

and rounded to the units.

The student obtains approval in the curricular unit in a normal season (continuous evaluation) if his final grade is greater than or equal to 9.5 values. The student who obtains a final grade greater than or equal to 18.5 values, must perform an oral proof of defense of note. If the student does not attend the oral test, the final grade will be 18 values.

**Appeal season**

The evaluation of the time of appeal consists in the performance of an examination, scheduled for this purpose. This exam consists of a written test, lasting between 2.5 and 3 hours, and which will evaluate all the contents taught in the curricular unit.

The examination of the appeal season is classified on a scale of 0 to 20 values. The final score is equal to the classification of the exam, rounded to the units.

The student obtains approval in the curricular unit if the final grade is greater than or equal to 10 values. The student who obtains a final grade greater than or equal to 18.5 values, must perform an oral proof of defense of note. If the student does not attend the oral test, the final grade will be 18 values.

**Note improvement**

Students approved in the curriculum unit who want to improve grade should, in advance, require this improvement from academic services.

In this case, they shall carry out the appeal examination on the only date provided for this at the time of appeal. Its final classification to the curricular unit will be replaced by the Exam note (rounded to the units), if it is superior to it.

**Other information**

Students should confirm that the email registered in CLIP is correct. Otherwise they may not receive important warnings.

For any test or exam, students must bring a blank exam notebook, writing material, calculating machine and document ID with photo.

In any situation not mentioned here, the Knowledge Assessment Regulation of the Faculty of Sciences and Technology of the New University of Lisbon shall apply, revised on 16 January 2018.

## Subject matter

**Short Programme**

1. Basic notions of probability.

2. Random variables and their probability distribution.

3. Moments of random variables.

4. Some important distributions.

5. Random vectors: Random discrete par and momentos.

6. Central Limit Theorem.

7. Rudiments on stochastic simulation7. Point estimation.

8. Parametric interval estimation.

9. Hypothesis testing: Parametric, Adjustment, Randomness.

10. Simple linear regression.