Statistical Methods

Code:

EA0021

Acronym:

ME

Keywords
Classification	Keyword
OFICIAL	Physical Sciences (Mathematics)

Instance: 2019/2020 - 2S

Active?	Yes
Responsible unit:	Mining Engineering Department
Course/CS Responsible:	Master in Environmental Engineering

Cycles of Study/Courses

Acronym	No. of Students	Study Plan	Curricular Years	Credits UCN	Credits ECTS	Contact hours	Total Time
MIEA	43	Syllabus since 2006/07	2	-	6	56	162

Teaching language

Portuguese

Objectives

The promotion of logical reasoning, methods of analysis and the theoretical development of mathematical concepts is fundamental to support the study of the majority of course units along this programme of studies.

This UC aims to ensure the acquisition of solid knowledge in the calculation of probabilities and statistics, considered an essential tool in many areas and situations of uncertainty, fundamental in Engineering. Another objective is to develop in students the ability to communicate accurate when referring to subjects that are based on concepts of Probability and Statistics. This UC also intends to develop a critical attitude when necessary to the analysis of statistical problems as well as the ability to apply the concepts acquired solving them. The acquisition of fundamental knowledge will give students the ability to acquire more advanced concepts that arise in the course and / or professional.

The student must be acquainted with basic notions on trigonometry, real functions, derivatives and integration.

The scientific component is 100%.

Learning outcomes and competences

At the end of this, students should be capable of: 
- Solve common problems involving basic theory of probability, random variables, probability distributions, random sampling, confidence intervals and hypothesis testing; 
- Explain and interpret the main statistical concepts; 
- Use descriptive statistics tools to analyse sample or populational data.

Working method

Presencial

Program

1. Brief review of concepts:
- Combinatorial Analysis;
- Theory sets.
2. Probability theory: events and probabilities, concepts definitions and applications.
3. Random variable: discrete and continuous variables, functions and probability distribution parameters, sums and n-dimensional distributions.
4. Distributions: Distributions theoretical discrete and continuous approximations and sums.
5. Descriptive Statistics: Sampling. Analysis, graphical representations, parameters and distribution of measurements;
6. Estimation: Point and interval estimators for normal populations and non- normal (central limit theorem and Tchebycheff’s inequality.
7. Hypothesis testing: Hypothesis testing parametric normal and non-normal populations.
8. Chi-square: independence and homogeneity adjustment.
9. Regression analysis and correlation.
10. Statistical data analysis using Microsoft Excel.

Mandatory literature

Apontamentos e demais documentação disponibilizados nos conteúdos da unidade curricular
Pestana, Dinis Duarte e Velosa, Sílvio Filipe; Introdução à Probabilidade e à Estatística, Fundação Calouste Gulbenkian, 2002
António Fiúza; Aquisição e Análise de Dados, Sebenta de apoio à UC do 3º Ano do Curso de Eng.ª de Minas, Publicação interna do Curso de Engenharia de Minas e Geoambiente, 2001

Complementary Bibliography

Ventsell; Théorie des probabilités, Editions Mir
Mood, Alexander M.; Introduction to the theory of statistics. ISBN: 0-07-042864-6
Athanasios Papoulis; Probability, random variables, and stochastic processes. ISBN: 0-07-100870-5
Rui Campos Guimarães, José A. Sarsfield Cabral; Estatística. ISBN: 978-84-481-5589-6
Paul L. Meyer; Probabilidade. ISBN: 85-216-0294-4
Malik e Mullen; A first course in probability and statistics, , Addison-Wesley
Douglas C. Montgomery, George C. Runger; Estatística aplicada e probabilidade para engenheiros. ISBN: 85-216-1360-1
Murteira, Bento José Ferreira; Probabilidades e estatística. ISBN: 972-9241-17-1
Hoel Paul G.; Introduction to mathematical statistics. ISBN: 0-471-80530-0

Teaching methods and learning activities

In class, concepts are presented and important results associated with an emphasis on geometric interpretations and practical applications. In order to clarify the definitions and theorems presented, several exercises are solved and illustrative applications are presented. The aim is to, whenever possible, the participation of students, not only in solving the exercises, but also in introducing new concepts. It remains to enhance the resolution of individual exercises and the guidance should be in the study of discipline and clarify questions that may arise in proposal exercises.

keywords

Physical sciences > Mathematics > Probability theory
Physical sciences > Mathematics > Statistics

Evaluation Type

Evaluation with final exam

Assessment Components

Designation	Weight (%)
Participação presencial	0,00
Exame	100,00
Total:	100,00

Amount of time allocated to each course unit

Designation	Time (hours)
Estudo autónomo	106,00
Frequência das aulas	56,00
Total:	162,00

Eligibility for exams

Gets frequency to this UC, in the current school year, every student that:
- Regularly registered in UC and does not exceed the maximum number of absences.

All students duly registered in UC, can perform the tests and examinations that are proposed and used for evaluation.

Regarding the assessment there are four different times, and they were the following:
1) Final Exam - to be marked;
2) Exam resource (E) (all matter) - to be marked.

Calculation formula of final grade

For the final grade of the UC student must have or be exempt from such frequency. In these conditions, any student can choose to get approved by final exam.

The final grade of UC is (scale 0-20):
- The grade of the final exam; 
- The grade of the exam recourse (E).

Special assessment (TE, DA, ...)

Students wishing to undertake improvement of classification may submit the evaluation defined for the UC according with existing regulations.

Classification improvement

Students who are under special statutes or having the or who have had previous years frequency, are exempt frequency. The approval can be obtained by performing the tests (T1, T2 and T3) or exam resource (E), the final classification is done according to the previous point.

Observations

Language of instruction: Portuguese.