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
Filipe José Gonçalves Pereira Marques, Paula Alexandra da Costa Amaral
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.
3 - Moments of random variables.
4 - Some important distributions. Central Limit Theorem.
5 - Point and interval estimation.
6 - Hypothesis testing.
7 - Simple linear regression
8 - R Introduction
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. Mood, A. M., Graybill, F. A. e Boes, D. C. (1974). Introduction to the Theory of Statistics, 3ªed. McGraw-Hill, New York
2. Murteira, B., Ribeiro, C. S., Silva, J. A. e Pimenta, C., (2002). Introdução à Estatística, McGraw Hill
3. Pedrosa, A. (2004). Introdução Computacional à Probabilidade e Estatística. Porto Editora
4. 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:
Module PS
1st test: 9 points (N1)
mini-test: 1 point (N2), accomplished in the theoretical-practical class
Module OR
2st test: 9 points (N3)
mini-test: 1 point (N4), accomplished in the theoretical-practical class
The first and second tests concern PS and OR, respectively, each quoting 9 points. The first and second mini-tests concern PS and OR, respectivel, yeach quoting 1 point. A student is considered approvedif it has a frequency note of Sufficient and the sum N1+N2+N3+N4 >=10. The final grade will be the value of this sum.
By final exam: Exam
Only students with frequency note of Sufficient can realize final exam (see date on the calendar of examinations).
Before the exam, the student indicates whether to be assessed in the two modules or just in one of the modules. In the latter case the classification obtained previously in the other module, shall be considered as the contribution for the classification of this module in the final exam. The student is considered approved if he has frequency note of Sufficient and final exam score of > = 10 points.
In the evaluation, students can use non-graphical calculator.