# Probability and Statistics D

## 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

12658

##### Credits

6.0

##### Responsible teacher

Luís Pedro Carneiro Ramos

##### Hours

Weekly - 4

Total - 71

##### 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

Participated theoretical-practical classes, with oral presentation of material and problem solving.

### Evaluation method

**Context**

The following guidelines on the Assessment Method are specifications for PE D in 2023-2024 of the Knowledge Assessment Regulation (RAC20) of FCT NOVA of 17 November 2020, which should be consulted in full by the Students (https://www.fct.unl.pt/estudante/informacao-academica).

**Frequency Obtaining**

In all Practical and Theoretical-practical classes, the presence of students will be indicated. Attendance will be attributed to students who are present at least 2/3 of the classes taught (see, pf, Article 6 §3 of RAC20). Absences will only be waived if they are legally justified. This rule is valid for all students, with the exception of:

a- students with student worker status, or any other recognized by the faculty''''''''''''''''s assessment and other valid rules of the Faculty.

b- students exempted from attending classes because they had previously obtained Frequency (for exact conditions, see, pf, Article 6 §4 of RAC20).

Students who, without legal justification, do not attend the first three classes of a Practical or Theoretical-Practical shift in which they are enrolled, may have their enrollment in the shift cancelled.

**Continuous evaluation**

Continuous assessment consists of carrying out three tests with a maximum duration of two hours, on dates and times published on CLIP. The three tests will have a classification T1, T2 and T3, given, in each one, by a grade between 0 and 20 values. The final grade of continuous assessment is calculated with T1, T2 and T3 using the formula with weights:

Final Grade = 0.4 T1 + 0.3 T2 + 0.3 T3.

For the purposes of entry on the agenda, the Final Score will be rounded to units.

The student obtains approval in the curricular unit in the normal period (continuous assessment) if his unrounded final grade is greater than or equal to 9.5 values. The student who obtains an unrounded final grade greater than or equal to 18.5 values, must take an oral exam to defend the grade. If the student does not attend the oral test, the final grade will be 18.

**Appeal Season**

The evaluation of the appeal period consists of carrying out an exam, on a date and time scheduled by the services that will appear in the CLIP. This exam consists of a written test, with a maximum duration of 3 hours, in which all the contents taught in the course will be evaluated.

The exam of the appeal season is classified on a scale from 0 to 20 values. For the purposes of entry on the agenda, the final grade is equal to the exam grade, rounded to 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 an unrounded final grade greater than or equal to 18.5 values, must take an oral exam to defend the grade. If the student does not attend the oral test, the final grade will be 18.

**Grade improvement**

Students approved in the curricular unit who intend to improve their grade must, in advance, request this improvement from the academic services.

In this case, they must take the appeal exam, on the only date scheduled for this at the time of appeal. Your final grade for the curricular unit will be replaced by the Exam grade (rounded to units), if this is higher.

Method of carrying out the assessment tests Except for any exceptional situation, all assessment tests will be carried out in person.

**Other information**

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

Email messages will only have a response every Wednesday/week.

Calculating machines allowed in the assessment tests must cumulatively meet the following conditions:

- be silent;

- do not require localized external power supply;

- do not have symbolic calculation (CAS);

- do not have the ability to communicate at a distance;

- do not have ribbons, rolls of paper or other printing media.

In any situation not mentioned here, the provisions of RAC20 apply.

## 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.

## Programs

Programs where the course is taught: