Introduction to Probability, Statistics and Operations Research
Code
10363
Academic unit
Faculdade de Ciências e Tecnologia
Department
Departamento de Matemática
Credits
6.0
Teacher in charge
Jorge Orestes Cerdeira, Maria de Fátima Varregoso Miguens
Weekly hours
6
Total hours
86
Teaching language
Português
Objectives
The main objectives are: a) to introduce students to the basic notions on statistics and probability. The students will be prepared to easily handle the requirements of a professional activity, concerning probabilities and statistics; b) introduce concepts from a few areas of Operations Research, namely Linear Programming, Integer Programming, Project Management and Decision Theory.
Prerequisites
Elementar knowledge about mathematical analysis, pointing out: elementar sets algebra, limit of sequences, primitives, integrals and real functions of one or more real variables. Elementar knowledge about Linear Algebra, namely, matrices, systems of linear equations and vector spaces.
Subject matter
Part I - Probability and Statistics.
1 - Basic notions of Probability.
2 - Random variables. Random vectors.
3 - Moments of random variables.
4 - Some important distributions. Central Limit Theorem.
5 - Point and interval estimation.
6 - Hypothesis testing.
Part II - Operational Research:
1 - Linear Programming:
1.1 - Formulations of Linear Programming problems.
1.2 - Graphical resolution.
1.3 - The Simplex method. Artificial Variable Technique.
2 - Integer Programming:
2.1 - Formulations of Integer Programming problems.
2.2 - Methods for solving Integer Programming problems.
3 - Project Management:
3.1 - Critical Path Method.
3.2 - PERT technique.
3.3 - Construction of the Time Chart and Resource Leveling.
3.4 - Reduction of the project duration.
4- Decision Theory:
4.1 - Decisions under risk and under uncertainty.
4.2 - Decision Trees.
Bibliography
Part I
1. Pedrosa, A. (2004). Introdução Computacional à Probabilidade e Estatística. Porto Editora
2. Murteira, B., Ribeiro, C. S., Silva, J. A. e Pimenta, C., (2002). Introdução à Estatística, McGraw Hill
3. Robalo, A. (1994). Estatística Exercícios. Vol I e II. Edições Sílabo
Part II
1. Wayne Winston, Operations Research: Applications and Algorithms, Duxbury Press; 4th. Edition, 2003
2. Introdução à Programação Linear, J.O. Cerdeira, texto de apoio à unidade curricular Introdução às Probabilidades e Estatística e Investigação Operacional, 2013
Teaching method
Classes operate on a theoretical and practical regime.
In classes are exposed the theoretical concepts, some demonstrations are carried out and simultaneously its application are illustrated through examples and exercises.
Pupils have supporting texts on all matter including exercises and application problems.
Substantial part of the study is done on learner autonomy, with the aid of notes and bibliographic other media, and with the support of teachers to answer questions at pre-established times.
Evaluation method
Evaluation rules
The u.c. consists of two modules: Probability and Statistics (PS) and Operational Research (OR), each with odds of 10 values.
Frequency: Obtained with at least two thirds of attendance in classes taught in each module.
Evaluation:
By tests:
Three tests to be carried during the school period. First and third tests concern PS and OR, respectively, each quoting 6. The second test comprises both PS and OR, each part quoting 4. A student is consideredapprovedif it has a frequency note of Sufficient and the sumof the tests scores >=10.The final gradewill be the valueof that sum.
By final exam:
Only students with frequency mark can realize final exam (see date on the calendar of examinations).
Before you take the exam, the student indicates whether to be assessed in two modules or module in which you want to be evaluated. In the latter case the classification obtained by testing in another module, shall be considered as the contribution of the classification of this module in the final exam. Considered approved if the student who obtains frequency and final exam score of > = 10 values.
The student with rating> = 18 values is subject to an oral examination in defense of the mark. No show for this test will involve a final score of 17 points.