Statistics and Probability

Code:

L.EC016

Acronym:

PE

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2025/2026 - 2S

Active?	Yes
Web Page:	https://sigarra.up.pt/feup/pt/ucurr_geral.ficha_uc_view?pv_ocorrencia_id=455265
Responsible unit:	Department of Civil and Georesources Engineering
Course/CS Responsible:	Bachelor in Civil Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L.EC	242	Syllabus	2	-	6	52	162

Teaching language

Portuguese
Obs.: Português

Objectives

JUSTIFICATION:
Essentially, two reasons justify the existence of this unit: the need to develop an analitical reasoning, scientifically based, the capacity of presenting arguments and of communicating in scientific and technical approaches in different domains of civil engineering; the need for acquiring scientific knowledge of probabilistic and statistical nature for use in the subjects that will be studied in the remaining semesters of the course, particularly in what concerns situations involving uncertainty and decision under uncertainty; skills for acting in the profession.

OBJECTIVES:
To induce an educational background for other following subjects in the curricula. To give solid knowledge for future developements at the specialization level as well as at the professsional level. To prepare the student for the use of probabilistic and statistical language and to be able to comunicate when dealing with subjects in which Probabilities and Statistics take part, ensuring that a correct interiorization of concepts is achieved. To educate the student to be able to translate his reasoning into mathematics when analysing real world problems and adequately formulate these problems. To educate the student in techniques that can be used in order to solve these problems. To be able to efiently use software for solving problems that require techniques or envolve statistical or probabilistic concepts. To be able to scientifically deal with situations and phenomena involving uncertainty and decision under uncertainty.

Learning outcomes and competences

RESPONSIBILITIES AND OUTCOMES OF LEARNING:
Development skills (CDIO): technical knowledge in basic sciences (ie in Statistics), personal and professional skills of thinking and problem solving engineering, experimentation and knowledge discovery, knowledge engineering and advanced skills and attitudes ; interpersonal communication skills (oral and written).
The student should be able to:
- Describe data sets by applying statistical techniques;
- Compute probabilities in complex situations, including those that use random variables of one or two dimensions, following or not typical distributions;
- Use the properties involved in the use of typical distributions;
- Solve estimation problems

- Apreend the philosophy of hypothesis testing

- Solve problems involving the goodness of fit of distributions and discuss their fitness
- Present arguments that justify a certain solution to a problem or to express a conclusion
- Choose the best solution or the best method, when faced with an ensemble of methods or solutions

Working method

Presencial

Pre-requirements (prior knowledge) and co-requirements (common knowledge)

The student should have knowledge of mathematics taught in previous semesters, for example, on the use of functions of one or more variables, sequences and series, and numerical analysis, including the use and implementation of calculations with the help of computers.

Program

1. Brief presentation of the statistical method in the context of Civil Engineering and uncertainty in Engineering.

2. The role of data.
2.1. different types of statistical variables
2.2. univariate distributions;
2.3. bivariate distributions

3. Probability spaces
3.1. generalization of concepts, axioms, and properties
3.2. independence of events and conditionning.

4. Unidimensional random variables:
4.1. discrete and continuous variables; 
4.2. brief reference to variable transformations;
4.3. mathematical expectation; moments
4.4. parameters of order.

5. Two-dimensional random variables:
5.1. joint distributions and conditional distributions
5.2. independence
5.3. mathematical expectation
5.4. 2nd order parameters

6. Typical distributions:
6.1. discrete
6.2. continuous 
6.3. properties of Gaussian law
6.4. other properties

7. Approximations of distributions:
7.1. approximations and convergency
7.2. Central Limit Theorem
7.3. most known approximations.

8. Estimation:
8.1. statistics, estimators e estimativas
8.2. estimators for the mean and the variance
8.3. estimation of the linear correlation coefficient
8.4. confidence intervals.

9. Hypothesis testing:
9.1. philosophy of testing
9.2. parameter testing
9.3. goodness of fit testing.

10. Initiation to the simple linear regression models.

DISTRIBUTION:
Scientific component: 80%
Technological component: 20%

DEMONSTRATION OF THE SYLLABUS COHERENCE WITH THE CURRICULAR UNIT'S OBJECTIVES:
The thematic of this curricular unit emphasize the need to develop a scientifically based reasoning, the capacity of presenting arguments and of communicating in scientific and technical approaches in different domains of civil engineering, in particular leading to the education to deal with uncertainty in engineering; the need for acquiring scientific knowledge of probabilistic and statistical nature for use in the subjects that will be studied in the remaining semesters of the course.

Mandatory literature

Douglas C. Montgomery, George C. Runger; Estatística aplicada e probabilidade para engenheiros. ISBN: 85-216-1360-1 (English original: Montgomery, Douglas C.;Applied Statistics and Probability for Engineers. ISBN: 0-471-17027-5 )
Paula Milheiro de Oliveira; Estatística - Colecção de exercícios, Feup (available in Moodle site)
Paula Milheiro de Oliveira; Estatística - Apontamentos da cadeira (Class notes available in the Moodle site)

Complementary Bibliography

Morais, M.C. ; Probabilidades e Estatística: Teoria, Exemplos & Exercícios (2a. edição), IST Press, 2023. ISBN: 978-989-8481-78-8, 2023
Paula Milheiro de Oliveira; Paulo Avilez Valente; Aprender Probabilidades e Estatística por Pequenos Projetos para Estudantes de Engenharia Civil, Efeitos gráficos, 2024. ISBN: 978-989-35360-4-9
Paulino, C.D. e Branco, J.A.; Exercícios de Probabilidade e Estatística, Escolar Ed, 2005
Moore, David S.; Introduction to the Practice of Statistics. ISBN: 0-7167-1989-4
Bento Murteira, C.S. Ribeiro, J.A. Silva. C. Pimenta; Introdução à Estatística, Escolar Editora, 2010
Pestana, Dinis Duarte; Introdução à probabilidade e à estatística. ISBN: 972-31-0954-9
Andreia Hall, Cláudia Neves, António Pereira; Grande maratona de estatística no SPSS. ISBN: 978-972-592-301-6
Alfredo H-S. Ang, Wilson H. Tang; Probability Concepts in Engineering: Emphasis on Applications to Civil and Environmental Engineering, Wiley, 2007

Teaching methods and learning activities

It is essentially a formative subject, coordinating fundamental theoretical knowledge with some approaches which are necessary in the subjects placed ahead in the curricula. At this level it is important to develop intuitive concepts as well as computational ability. The concepts are exposed in a clear and objective way, making frequent use of examples of physical or geometrical nature. The use of statistical software is encouraged, as a working tool, namely through the execution of 2 working projects in the computer room . Sessions are held in the computer rooms.

DEMONSTRATION OF THE COHERENCE BETWEEN THE TEACHING METHODOLOGIES AND THE LEARNING OUTCOMES:
The teaching methodologies allow the students be able to describe data sets by applying statistical techniques, compute probabilities in complex situations, including those that use random variables of one or two dimensions, following or not typical distributions, use the properties involved in the use of typical distributions solve estimation problems, solve problems involving the goodness of fit of distributions and discuss their fitness, learn the philosophy of hypothesis testing.

Software

R - R studio
Excel
SPSS

keywords

Physical sciences > Mathematics > Probability theory
Physical sciences > Mathematics > Applied mathematics > Engineering mathematics
Physical sciences > Mathematics > Statistics

Evaluation Type

Distributed evaluation with final exam

Assessment Components

Designation	Weight (%)
Exame	75,00
Trabalho prático ou de projeto	25,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	110,00
Frequência das aulas	52,00
Total:	162,00

Eligibility for exams

Approval of the course unit implies compliance with the attendance requirement, considering that a student complies with this requirement if, having been regularly enrolled, they do not exceed the limit of 25% of absences from the face-to-face classes scheduled for each type. In addition to the cases provided for in the FEUP rules in force, students who have obtained a final grade of 6 or higher in the course in the immediately preceding academic year are exempt from the attendance requirement.

Calculation formula of final grade

CP: mean classification in the 2 working projects (rounded to one decimal)

CE: classification in the writing paper (rounded to one decimal)


final classification = 0,250 * CP + 0,750 * CE


NOTE 1: Obtaining a grade lower than 5.5 in the first working project prevents the student from completing the second working project. In other words, 
in order to obtain a valid grade in the distributed assessment, the student must obtain a grade of no less than  5.5 in the first working project.

NOTE 2: The distributed evaluation ran in the previous course can be transfered on demand until a deadline that will be further noticed.

NOTE 3:  No delivery of the working projects results in "zero" mark in the associated component. Working projects take place exclusively in the period up to the last day of classes and will not be repeated at any time later.

Examinations or Special Assignments

The two working projects mentioned above (TPs) are done during laboratory sessions, to be announced (see moodle).

Project work cannot be carried out after the last day of classes, and students who have not done so will score zero in this component. The same formula is used to calculate the grade as above, so the student will take a weight of 100% in the written exam.

 

Special assessment (TE, DA, ...)

Final written exam for the Written Exam Component. For the component regarding the working projects the assessment made along the academic semester remains valid.

Students benefiting from special status have also to submit to the evaluation regarding the distributed component, and must held during the semester lectures at a date and hour to be assigned.
Students that may be candidates to special exams have to do this component no later than that date, otherwise their mark in this component to be introduced in the formula  of the special exam will be zero. This is equivalent to having a 100% weight in the Written Exam.

Classification improvement

Final written exam for the Written Exam Component. For the component regarding the working projects the assessment made along the academic semester remains valid.
The previous general formula for calculating the grade applies. Project work cannot be repeated.

Observations

During any assessment, the possession of any electronic device (e.g. mobile phones, tablets, headphones, smartwatches, etc.) is strictly prohibited, with the exception of those expressly indicated by the teaching staff.
It is the student's responsibility to anticipate this situation before the start of the assessment.