Publication in the Diário da República: Despacho nº 14433/2024 - 05/12/2024
4 ECTS; 1º Ano, 2º Semestre, 30,0 PL + 30,0 TP + 3,0 OT , Cód. 912312.
Lecturer
- Maria Manuela Morgado Fernandes Oliveira (1)(2)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Curriculum content for secondary school mathematics subjects, including Linear Algebra, Mathematical Analysis I, and Mathematical Analysis II.
Objectives
Understanding basic concepts of statistics and probability.
Analyzing univariate and bivariate data.
Applying estimation and probability.
Determining roots of nonlinear equations.
Solving systems of nonlinear equations and integrals using numerical formulas.
Program
Course Content
1. Exploratory Data Analysis
2. Introduction to Probability
3. One-Dimensional Random Variables
4. Theoretical Distributions
5. Introduction to Estimation
6. Bivariate Data Analysis
7. Nonlinear Equations and Systems of Equations
8. Numerical Integration
Detailed Course Content
1. Exploratory Data Analysis
1.1. General notions and examples of statistical applications.
1.2. Fundamental statistical terms and concepts.
1.3. Frequency Distributions and Graphical Representation of Univariate Data.
1.4. Sample Characteristics.
1.5. Other Graphical Representations.
2. Introduction to Probability
2.1. Random experiments. Sample space. Events.
2.2. Probabilities of an event. Properties.
2.3. Conditional probability.
2.4. Independent events and mutually exclusive events.
2.5. Multiplication theorem. Theorem of Total Probabilities. Bayes' theorem.
3. One-Dimensional Random Variables
3.1. Discrete and continuous random variables.
3.2. Distribution function. Properties.
3.3. Probability mass function and probability density function.
3.4. Parameters of a Distribution. Properties.
4. Theoretical Distributions
4.1. Discrete Probability Distributions and Continuous Probability Distributions.
4.2. Weak Law of Large Numbers and Central Limit Theorem.
5. Introduction to Estimation
5.1. Preliminary notions about estimation. Estimators and estimates.
5.2. Point estimation. Some point estimators.
5.3. Interval Estimation
6. Bivariate Data Analysis
6.1. General Concepts
6.2. Measures of Association
6.3. Scatter Plot
6.4. Linear Association Analysis
6.5. Linear Regression
6.6. Model Hypotheses
6.7. Estimation of Model Parameters
6.8. Prediction with the Regression Line
6.9. Goodness of Fit
7. Nonlinear Equations and Systems of Equations
7.1. Root Finding
7.2. Iterative Methods
7.3. Newton's Method for Systems of Nonlinear Equations
8. Numerical Integration
8.1. Newton-Cotes Formulas
Evaluation Methodology
i) Assessment by Attendance
During the semester, the student must complete:
- 3 written exams graded from 0 to 20 points (PE1, PE2, and PE3), whose final grade (CF)
is CF = 0.35PE1 + 0.35PE2 + 0.30PE3.
or
- 3 written exams graded from 0 to 20 points (PE1, PE2, and PE3) and an individual oral presentation of two assignments (T1 and T2), graded from 0 to 20 points, and the final grade (CF)
is CF = 0.30PE1 + 0.30PE2 + 0.30PE3 + 0.05T1 + 0.05T2
- The student is exempt from the exam if they obtain at least 2 points in each of the written exams and the final grade is equal to or greater than 9.5 points.
ii) Assessment by Exam
- Taking an exam.
The exam consists of a written test, graded from 0 to 20 points.
The student passes the course if the final exam grade is equal to or greater than 9.5.
The student obtains approval in the course unit in accordance with the provisions of Points 11 and 12 of Article 11 of the IPT Academic Regulations.
The indicated assessments also apply to working students.
Bibliography
- Maroco, J. (2018). Análise Estatística com o SPSS Statistics. Lisboa: ReportNumber
- Pestana, D. e Velosa, S. (2010). Introdução à Probabilidade e à Estatística. Lisboa: Fundação Calouste Gulbenkian
- Pina, H. (2010). Métodos Numéricos. Lisboa: Escolar Editora
- Santos, F. (2002). Fundamentos de Análise Numérica. Lisboa: Sílabo
Teaching Method
Lectures (TP) are expository, introducing fundamental concepts and presenting application examples. Practical classes (PL) present and consolidate knowledge through problem-solving exercises. Tools used: calculator, Excel, Wolfram Alpha, and GeoGebra
Software used in class
The Moodle platform is used, and occasionally the Excel spreadsheet and the IBM SPSS statistical package are used to solve some exercises. The Wolfram Alpha (https://www.wolframalpha.com/) and Geogebra (https://www.geogebra.org/) platforms are also used.
