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Presentation
Presentation
The main objective of the Probability and Statistics course is to provide students with fundamental concepts of probability theory and techniques of descriptive statistics and statistical inference that are essential to engineering studies.
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Class from course
Class from course
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Degree | Semesters | ECTS
Degree | Semesters | ECTS
Bachelor | Semestral | 6
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Year | Nature | Language
Year | Nature | Language
1 | Mandatory | Português
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Code
Code
ULHT6638-24496
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Prerequisites and corequisites
Prerequisites and corequisites
Not applicable
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Professional Internship
Professional Internship
Não
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Syllabus
Syllabus
1. Descriptive Statistics Types of data: integer, continuous, categorical, etc. Frequency tables Measures of central tendency and dispersion Data visualization (bar charts, histograms, box plots, etc.) 2. Linear Regression Independent and dependent variables Scatter plots Covariance and Pearson correlation coefficient Regression line Residuals and the least squares method Estimation of the response for a given value of the independent variable 3. Probability Theory Random experiment. Sample space. Event. Operations on events Properties of the probability function. Probability of the union of events Law of total probability. Bayes' theorem Conditional probability. Independent events 4. Distributions Random variable Bernoulli discrete distribution Normal continuous distribution 5. Statistical Inference Sample and random sample Estimator and estimate of a proportion Confidence interval and hypothesis test for a proportion
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Objectives
Objectives
This course unit enables students to: LO1: understand probability as a measure function that is essential to science. LO2: understand statistics as a field of science that enables engineering to collect and analyse data, formulate hypotheses about those data, and test those hypotheses. In this sense, statistics and probability are essential to knowledge and engineering.
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Teaching methodologies
Teaching methodologies
Theoretical concepts are introduced in class and complemented with practical real-world examples. Students are encouraged to solve exercises and to raise any questions they may have. For each topic, a set of exercises is provided to apply the theoretical concepts. Students are guided through the solution process, and the final solutions are subsequently presented. Supporting materials and exercises with suggested solutions will be made available on Moodle. Continuous assessment, adapted to students' progress, is considered good practice. Individual support and availability to clarify any questions whenever necessary are essential to students and their academic performance. .
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References
References
Apontamentos e séries de exercícios disponibilizados na plataforma moodle. Murteira, B. (2012), Probabilidades e Estatística, vols. I e II MacGraw-Hill. Murteira, B. (2007), Introdução à Estatística, MacGraw-Hill. Morais, M.C. (2020). Probabilidades e Estatística: Teoria, Exemplos & Exercícios. IST Press (Coleção Ensino da Ciência e da Tecnologia). Ross, S. M. (2014). Introduction to Probability and Statistics for Engineers and Scientists. 5th ed, Academic Press
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Assessment
Assessment
É exigida a presença de cada aluna(o) a pelo menos 75% das aulas práticas de modo a ter a oportunidade de fazer avaliação contínua. Caso contrário, só se poderão apresentar a avaliação em época de recurso. Trabalhadores- estudantes não são contemplados com esta regra.
A avaliação conta com uma componente contínua, que consiste na realização de 2 testes ou um exame (Frequência Final ou Recurso). Existe nota miníma para cada teste de 7,0 valores (escala de 0 a 20 valores).
Média dos 2 testes = A Nota de Exame = B
- Se A > 9,5 o(a) aluno(a) está aprovado à UC e poderá fazer exame se quiser melhorar a nota. Neste caso, a Nota Final = max(A,B)
- Se A < 9,5 o(a) aluno(a) está reprovado à UC e terá de fazer exame se quiser obter aprovação à UC. São considerados aprovados os alunos que obtenham nota final não inferior a 10 valores
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Mobility
Mobility
No
