Probability and Statistics

Code:

M2043

Acronym:

M2043

Keywords
Classification	Keyword
OFICIAL	Mathematics

Instance: 2025/2026 - 1S

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

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
L:BIOINF	30	Official Study Plan	2	-	6	48	162

Teaching language

Portuguese

Objectives

Acquisition of basic concepts of Probability and Statistics and their application to concrete situation.
Particular attention is paid to the presentation and understanding of the concepts, keeping the mathematical treatment on an medium level.

Learning outcomes and competences

On completing this curricular unit it is expected that the student:

1. can understand the concepts involved in a statistical study and be aware of the various problems that arise in each particular study.
2. can identify and apply appropriate techniques of descritive statistics to organize and summarize data and interpret them;
3. dominates the probability calculus and knows to calculate probabilities associated with the phenomenon under study;
4. be able to characterize random variables/random vectors and identify the respective probability distributions;
5.  be able to make inferences on population parameters applying techniques of point and interval estimation.

Working method

Presencial

Program

1. Introduction to the objectives and methodology of Statistics
(Statistical variables; Population and sample; Sampling techniques; Experimental and observational studies);

2. Descriptive Statistics and exploratory data analysis: definition of statistics, fundamental concepts, types of observations and measurement scales, data summarization techniques (tables, graphs, location and dispersion measures), definition of outlier and concept of correlation.

3. Probability Theory: fundamental concepts, interpretations of the concept of probability, independence of events and conditional probability, Bayes and total probability theorems.

4.Random variables: characterization, discrete and continuous models, two-dimensional random variables, function of a random variable; Central Limit theorem and its applications. Sampling distributions.


6.Statistical Inference: basic properties of estimators, confidence intervals.

Mandatory literature

Douglas C. Montgomery; 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

All support material is available on the uc page on MoodleUP.

Software

R

keywords

Physical sciences > Mathematics > Statistics

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	114,00
Frequência das aulas	48,00
Total:	162,00

Eligibility for exams

No requirements.

Calculation formula of final grade

In both evaluation periods, the classification will be that obtained in an exam with a score of 20 points, with the exception described below.

Exception applicable to both periods: Students with a classification greater than or equal to 17.5 may have to take a written or oral test to obtain a classification greater than or equal to 18. Otherwise, they will receive a rating of 17 values.

Special assessment (TE, DA, ...)

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

Observations

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."

 

A qualquer aluno pode ser exigida a realização de uma prova oral para esclarecer dúvidas que tenham surgido relativamente às provas ou trabalhos de avaliação.