Introduction to Probability, Statistics and Operations Research

General characterization

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.

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

Available soon

Evaluation method

The u.c. consists of two modules: Probability and Statistics (PS) and Operational Research (OR)​​, which will be evaluated independently, each one for a maximum value of 10 points. All the evaluation tests and exams are in person unless the pandemic situation does not allow it.

Attendance

Due to the pandemic situation all students are dismissed from class attendance.

Continuous Evaluation

The studens are evaluated in both modules PS and OR in the date defined by FCT-UNL.

Module PS: the maximum grade is 10 points. Let N1 be the grade obtained by the student.

Module OR: the maximum grade is 10 points. Let N2 be the grade obtained by the student.

The final classification will be equal to N1+N2 rounded up to the units.

A student passes the course if he/she complies with the requirement N1+N2>=9.5. Students that grade N1+N2>=17 may be called to perform an additional examination. Students in such conditions that fail this additional examination will be evaluated with a final grade of 16 points.

Exam

Students who have not been approved during the continuous evalutaion may take the final exam

Prior to the exam, the student must indicate whether he/she wishes to be evaluated in the two modules (full exam) or just in one of the modules. In the latter case, the new module classification replaces the old one and the final grade is recomputed accordingly. Again, the student passes the course if N1+N2 >=9.5. Students that grade N1+N2>=17 may be called to perform an additional examination. Students in such conditions that fail this additional examination will be evaluated with a final grade of 16 points.

Already approved students (grade improvement):

Those students who have already passed the course are eligible for course grade improvement via the final exam, in which case they must sign up beforehand in the "Serviços académicos" or CLIP. In addition, students should be aware that for course grade improvement both modules need to be assessed and therefore they should prepare themselves accordingly. Students that grade N1+N2>=17 may be called to perform an additional examination. Students in such conditions that fail this additional examination will be evaluated with a final grade of 16 points. The student’s final course grade will be the maximum between the grade obtained in the exam and the one obtained via continuous evaluation.

Materials

During any evaluation students are only allowed to use a scientific calculator.

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.

Programs

Programs where the course is taught: