# Introduction to Probability, Statistics and Operations Research

## 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.

## General characterization

10363

6.0

##### Responsible teacher

Isabel Cristina Silva Correia, Vanda Marisa da Rosa Milheiro Lourenço

Weekly - 6

Total - 86

Português

### 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

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.

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: