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Probability and Statistics

Code:

LTE22121

Sigla:

PE

Áreas Científicas
Classificação	Área Científica
OFICIAL	Matemática

Ocorrência: 2021/2022 - 2S

Ativa?	Yes
Página Web:	https://moodle.ips.pt/2122/course/view.php?id=300
Unidade Responsável:	Departamento de Matemática
Curso/CE Responsável:

Ciclos de Estudo/Cursos

Sigla	Nº de Estudantes	Plano de Estudos	Anos Curriculares	Créditos UCN	Créditos ECTS	Horas de Contacto	Horas Totais
LTE	37	Plano de Estudos	2	-	6	60	162

Língua de trabalho

Portuguese

Objetivos

- Apply the concepts of random variable and its distribution;
- Solve problems involving models and probability distributions with discrete variables and with continuous variables;
- Understand the concept of random sample and solve problems involving sampling distributions;
- Characterize and apply estimators;
- Construct and interpret confidence intervals;
- Identify and apply the appropriate hypothesis test;
- Identify the relation between hypothesis testing and confidence intervals;
- Build and analyze a simple linear regression model.

Resultados de aprendizagem e competências

The curricular unit contents are structured, regarding its suitability for the intended learning outcomes. Therefore, each subject approaches fundamentals concepts and practical applications by solving problems using the basic tools of Probability and Statistics to enable students to analyze certain phenomena of random nature, framed in the context of technology, particularly in the recognition and enforcement of probabilistic models, the deduction and application of confidence intervals and hypothesis testing, and the construction and analysis of simple linear regression models.

Modo de trabalho

Presencial

Programa

1. Random Variables: Concept of r.v. Functions for discrete and continuous r.v Expected value, variance and standard deviation, characterization and properties
2. Theoretical Distributions (TD): Discrete DT; Binomial and Poisson; Characterization. Continuous DT; Exponencial, Uniform and Normal. Brief reference to the Student-t, Chisquare and Snedecor F DT properties
3. Elements of Sampling Theory: Population and sample. Random Sample and Statistic. Sampling. Distribution.
4. Elements of Estimation Theory: Concept of Estimator; properties. Point and Interval Estimates. Confidence intervals.
5. Hypothesis Testing (HT): Null and alternative hypothesis, critical region, significance level, decision rule of the test, errors type I and type II and power of the test. Parametric HT of normal populations.
6. Simple Linear Regression: Regression line. Parameter estimation of best linear fit using the least squares approach. Concept of residuals. Empirical linear correlation coefficient.

Bibliografia Obrigatória

Montgomery, D.; Runger, G., ; Applied statistics and probability for engineers, John Wiley & Sons. ISBN: 9781119585596
Murteira, B.; Antunes, M; Probabilidades e Estatística, Lisboa: Escolar, 2012. ISBN: 978-972-592-359-7
Murteira, B.; Ribeiro, C. S.; Andrade e Silva, J.; Pimenta, C.; Introdução à Estatística, Escolar Editora, 2015. ISBN: 9788448160692

Bibliografia Complementar

André, J; Probabilidades e Estatística para Engenharia, Lidel, 2018. ISBN: 9789897522703
Galvão de Melo, F.; Probabilidades e Estatística: conceitos e métodos fundamentais, Escolar Editora. ISBN: 9789725921104
Reis, E. .[et al.]; Estatística Aplicada - Volume I e II, Edições Sílabo, 2003. ISBN: 9789726189862
Robalo, A.; Estatística - Exercícios, Volumes 1 e 2, Edições Sílabo, 2001. ISBN: 9789726189121, 9789726189367

Métodos de ensino e atividades de aprendizagem

- Classroom lectures through a combination of lecture method and problem solving;
- E-learning in the Moodle platform, providing access to the contents of UC through slides, videos, and solved and proposed exercises, promoting the holding of weekly activities.

Methodologies used are centered on knowledge of concepts and their applications.
With the classroom lectures are promoted the transmission of probability and statistical contents and its application through problem solving, mostly in contexts related to technology.
E-learning methodology, promotes discipline and autonomous work throw the weekly activities proposed, deepening the probability and statistical contents covered.

Tipo de avaliação

Distributed evaluation without final exam

Componentes de Avaliação

Designation	Peso (%)
Teste	100,00
Total:	100,00

Componentes de Ocupação

Designation	Tempo (Horas)
Estudo autónomo	102,00
Frequência das aulas	60,00
Total:	162,00

Obtenção de frequência

There are two ways of assessment: by Tests and by Exam.

Continuous Assessment (or by Tests)

Continuous assessment is based on two (2) tests.
Designating by MT the average of the classifications of the 2 tests, the final classification (CF) will be rounded up to the units of the following value:
CF = MT = 0.5*T1+0.5*T2
The conditions for approval in the continuous assessment are as follows:
1. If CF (rounded to units) is greater than or equal to 10 and less than 18, the student is approved with a final grade equal to CF (rounded to units), provided that in any of the tests the score was greater than or equal to 6.5;
2. If CF (rounded to the nearest unit) is greater than or equal to 18, the student will have to take an oral exam, the final grade being the average of these two grades. If you do not attend the oral test, the final classification will be 17 values.
3. If the tests are carried out remotely, the maximum score that the student can obtain without undergoing an oral test will be 15 values.

To retrieve a test:
In order to pass a student with a score greater than or equal to 8.0 in one of the tests can retrieve the test with the lowest grade. A student who has less than 8.0 in one of the tests, who was not able to perform a test or has given up in one test can only recover that test.
The recovery of a test takes place at the exact day and time of the Normal Exam and in order to do so the student must enroll in due time.

4. To calculate CF: if one of the tests is less than 6.5 and the average of the testes is greather than or equalnto 18, the gradeto be awarded will be 9. 


Exam-based Assessment

Students who choose not to take the continuous assessment or have not obtained approval can attend the regular exams.
The exam-based assessment is subject to the following conditions:
1. If the exam grade (rounded to the units) is greater than or equal to 10 and less than 18 the student will pass with a final grade equal to the exam grade;
2. If the exam grade is greater than or equal to 18 the student will have to take an oral test and the final grade will be the average of the classifications of oral test and the exam (otherwise, the final grade will be 17)
3. If the exams are carried out remotely, the maximum score that the student can obtain without undergoing an oral exam will be 15 values.

Fórmula de cálculo da classificação final

Continuous Assessment (or by Tests)

• CF  = 0.50*T1+0.50*T2

 

Exam-based Assessment

• CF = Exam Grade