Statistics and Probability
Instance: 2011/2012 - 1S
Cycles of Study/Courses
Teaching - Hours
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.
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)
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
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
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.
Distributed evaluation with final exam
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.
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.