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# Statistics and Probability

 Code: EEC0011 Acronym: PEST

Keywords
Classification Keyword
OFICIAL Mathematics

## Instance: 2011/2012 - 1S

 Active? Yes Responsible unit: Department of Electrical and Computer Engineering Course/CS Responsible: Master in Electrical and Computers Engineering

### Cycles of Study/Courses

Acronym No. of Students Study Plan Curricular Years Credits UCN Credits ECTS Contact hours Total Time
MIEEC 357 Syllabus (Transition) since 2010/2011 2 - 6 63 162
Syllabus 2 - 6 63 162

### Teaching - Hours

 Lectures: 2,00 Recitations: 2,00
Type Teacher Classes Hour
Lectures Totals 2 4,00
Daniel Enrique Lucani Rotter 2,00
Jaime dos Santos Cardoso 2,00
Recitations Totals 8 16,00
Jaime dos Santos Cardoso 4,00
Luís António Pereira de Meneses Corte-Real 8,00
Daniel Enrique Lucani Rotter 4,00

Portuguese

### Objectives

This course aims to endow students with underlying knowledge of Statistics and Probability, which is indispensable to take decisions in uncertainty situations that happen in various areas of Engineering.
This course also aims to endow students with accurate communication skills when themes in the domain of Statistics and Probability are referred. Students will also develop a critical attitude in the analysis of engineering problems and they will be able to apply their knowledge in the resolution of practical problems. The adequate learning of the fundamental concepts of this course will make students able to easily learn advanced knowledge in their future career, both academic and professional.

### Program

1) Probabilities
Conditional probability and independence; Bayes’ theorem

2) Random Variables
One-dimensional and multidimensional random variables; functions of random variables; most important distributions (discrete and continuous)

3) Sampling
Samples and sampling distributions

4) Point estimate
Estimators and estimates; desirable properties if point estimates; estimation methods (method of least squares)

5) Interval estimate
Concept of confidence interval; specification of confidence intervals; sampling dimensioning;

6) Hypothesis testing
Introduction; hypothesis testing procedures; relationship between confidence intervals and hypothesis testing; dispersion and localization testing

7) Introduction to stochastic processes
Notion of discrete stochastic processes; average and correlation of a discrete stochastic process; stationary stochastic processes; ergodic stochastic processes; white noise; Wiener’s model

### Mandatory literature

Douglas C. Montgomery, George C. Runger; Applied statistics and probability for engineers. ISBN: 0-471-74589-8
Douglas C. Montgomery, George C. Runger; Estatística aplicada e probabilidade para engenheiros. ISBN: 85-216-1360-1

### Complementary Bibliography

Papoulis, Athanasios; Probability, random variables, and stochastic processes. ISBN: 0-07-100870-5
Guimarães, Rui Manuel Campos; Estatística. ISBN: 978-84-481-5589-6
Meyer, Paul L.; Probabilidade. ISBN: 85-216-0294-4
Isabel Ferreira; Probabilidades e Estatística, 2007
Ronald E. Walpole, Raymond H. Myers, Sharon L. Myers, Keying Ye; Probability and Statistics for Engineers and Scientists, Pearson Education International
Dimitri P. Bertsekas and John N. Tsitsiklis; Introduction to Probability, Athena Scientific

### Teaching methods and learning activities

Theoretical-classes: presentation of the themes of the course illustrated by examples, which explain the concepts and results presented;

Theoretical-practical classes: exercises proposed and solved by the professor. Students will be encouraged to actively participate in class by suggesting solutions to the exercises and by criticizing results.

### Evaluation Type

Distributed evaluation with final exam

### Assessment Components

Description Type Time (hours) Weight (%) End date
Attendance (estimated) Participação presencial 56,00
Total: - 0,00

### Eligibility for exams

Students have to attend to classes (they cannot miss more than three theoretical-practical classes), according to Article 4, Paragraph 1 of General Evaluation Rules of FEUP.

According to number 3 of paragraph 4 of General Evaluation Rules of FEUP, students with a special status (working-students, military personnel) do not need to attend to classes. Students who attended to this course in 2008/2009 do not need to attend classes either, and it will be considered their continuous assessment mark.

### Calculation formula of final grade

FM= 0,4* CA + 0,6 * FE

FM- Final Mark (from 0 to 20)
FE- Final Exam (from 0 to 20)
CA- Continuous Assessment (from 0 to 20)

Students have to reach a minimum mark of 30% in the final exam to complete the course (6 out of 20).
Continuous assessment will be based on 5 exercises.

### Special assessment (TE, DA, ...)

Students who do not need to attend classes and that opt not to take the continuous assessment component, or who do not want to keep their 2010/2011 continuous assessment mark, are admitted to exams, being their final mark the mark of the exam.

### Classification improvement

Students can improve their marks by attending to a new exam, which will take place at the two following seasons. It may include an extra exercise related to the continuous assessment component.