Probability and Statistics

Code:

M2022

Acronym:

M2022

Level:

200

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2022/2023 - 2S

Active?	Yes
Responsible unit:	Department of Mathematics
Course/CS Responsible:	Bachelor in Physics

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:F	13	Official Study Plan	2	-	6	56	162

Teaching language

Portuguese

Objectives

Acquisition of basic concepts of Probability and Statistics and their application to concrete situations.

Learning outcomes and competences

be able to identify and formulate a problem, to choose adequate statistical methods and to analyze and interpret in a critical way the obtained results.

Working method

Presencial

Program

1. Brief introduction to the objectives and methodology of statistics.

2. Descriptive Statistics: definition of a statistic, types of observations and measurement scales; techniques for summarizing data (tables, graphs, measures of location and dispersion), outlier definition and the concept of correlation. 

 

3. Some probability distributions: discrete distributions (uniform, binomial, and Poisson) and continuous (uniform, normal, exponential, chi-square and t-student. F); de Moivre-Laplace and the Central Limit theorems.

 

4. Random variables: discrete and continuous cases, distribution, mean and variance. Some probability distributions: discrete (uniform, binomial) and continuous (uniform, normal, chi-square, t-student and F) distributions; Central Limit theorem.

 

5. Sample distributions.

6. Statistical inference:point estimation (main concepts and properties of estimators);  interval estimation (confidence intervals for the mean, difference in means, proportion, difference in proportions, variance); introduction to hypothesis testing.

Mandatory literature

Montgomery Douglas C.; Applied statistics and probability for engineers. ISBN: 0-471-20454-4
Christopher J. Wild; Chance encounters. ISBN: 0-471-32936-3
Bento José Ferreira Murteira; Introdução à estatística. ISBN: 972-773-116-3

Complementary Bibliography

Myra L. Samuels; Statistics for the life sciences. ISBN: 978-0-13-122811-5 0-13-122811-0

Teaching methods and learning activities

Contact hours are divided into theoretical and theoretical-practical classes. In the first, the contents of the program are presented, using various examples to illustrate the topics covered and to motivate and guide the students' autonomous study. In theoretical-practical classes exercises and problems are solved and discussed. In particular, datasets are analysed, whenever possible using the R software. Support materials are available on the course page on MoodleUP.

Software

R (opcional)

keywords

Physical sciences > Mathematics > Statistics
Physical sciences > Mathematics > Probability theory

Evaluation Type

Evaluation with final exam

Assessment Components

designation	Weight (%)
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	52,00
Trabalho escrito	4,00
Total:	162,00

Eligibility for exams

There are no restrictions.

Calculation formula of final grade

The approval of the course can be obtained

1) by performing two tests. In this case, it is mandatory
a) to obtain a minimum score of 7 points (out of 20 points) in each of them and

b) the weighted average (see calculation *) of the marks obtained in the two tests must be greater or equal to 10 points.


* In this case, the final classification of the student is 0.5xT1+0.25xT2+0.25xT3 where,

T1=classification of the first test,  T2=classification of the second test and T3=classification of the third  test. 

Only students who have obtained a mininum score of 7 point  (out of 20 points) in the 1st test can take the 2nd test. Of these, only students who have obtained a mininum score of 7 point  (out of 20 points) in the 2nd test can take the 3rdd test.

2) by final exam (normal time or resource).

Students who have passed the course for the tests and have not obtained the desired result can take the normal period exam. In this case, students will have to choose, at the time of delivery of the exam, to do away with the classification already obtained in the evaluation by tests (indicating in the exam the desired option).

 

Students with a final mark of 17.5 values  or higher (obtained in the tests or in any of the exam periods) may have to perform a complementary written or oral exam in order to obtain a score greater than or equal to 18 values.

Examinations or Special Assignments

The exams required under special statutes will consist of a written (or oral) exam which may be preceded by an eliminatory oral exam.

Special assessment (TE, DA, ...)

Exams under speacial conditions will consist of a written test which can be preceded by an oral eliminatory exam.

Classification improvement

Improvement in the classification can be obtained in the second call only.

Observations

Any student may be required to take an oral examination should there be any doubts concerning his/her performance on certain assessment pieces,

Course Jury: Maria João Costa 

Artigo 13º do Regulamento Geral para Avaliação dos Discentes de Primeiros Ciclos, de Ciclos de Estudos Integrados de Mestrado e de Segundos Ciclos da U.Porto, aprovado em 19 de Maio de 2010 (cf. http://www.fc.up.pt/fcup/documentos/documentos.php?ap=3&ano=2011): "A fraude cometida na realização de uma prova, em qualquer das suas modalidades, implica a anulação da mesma e a comunicação ao órgão estatutariamente competente para eventual processo disciplinar."