Publication in the Diário da República: Despacho n.º 15239/2016 - 19/12/2016
5 ECTS; 1º Ano, 2º Semestre, 30,0 T + 30,0 TP
- Maria Manuela Morgado Fernandes Oliveira
This course aims to ensure:
a) the recovery and consolidation of knowledge of Probabilities and Descriptive statistics;
b) the acquisition of knowledge about random variables and some theoretical probability distributions (discrete and continuous);
c) the acquisition of knowledge and the development of mathematical skills in the scope of estimation (point and interval) and the decision on conditions of uncertainty;
d) Proceed to data analysis, interpret the results and carry out a decision;
e) access to inclusive, quality and equitable education and, promote opportunities for lifelong learning for all. (Sustainable Development Goal 4, according to the 2030 Agenda for Sustainable Development, adopted by the United Nations General Assembly in September 2015).
1. DESCRIPTIVE STATISTICS
1.1. Basic Concepts.
1.1.1.Population and sample.
1.1.2.Phases of the statistical method.
1.2.Type of data.
1.3.Distribution of frequencies and graphical representation of data.
1.4.Measures of descriptive statistics.
1.4.1. Location measures: central tendency and order (quartiles). Identification and classification of outliers. Diagram of extremes and quartiles.
1.4.2. Dispersion measures.
1.4.3. Asymmetry measures.
1.4.4. Flattening or kurtosis measures.
2. INTRODUCTION TO THE THEORY OF PROBABILITIES
2.1. Some notes on combinatorial analysis.
2.2. Basic concepts.
2.2.1. Random experience.
2.2.2. Results space.
2.3. Algebra of events.
2.3.1. Complementary event.
2.3.2. Union of events.
2.3.3. Intersection of events.
2.3.4. Difference of events.
2.3.5. Properties of operations between sets
2.4. Probability laws.
2.4.1. Classical (or Laplace) definition of probability.
2.4.2. Frequent or empirical definition.
2.4.3. Axiomatization of probability theory
2.5. Conditioned probability.
2.6. Independent Events
2.7.The total probability theorem and Bayes' theorem
3. RANDOM VARIABLES AND THEORETICAL DISTRIBUTIONS OF PROBABILITY
3.1. Random variable definition
3.2. Discrete random variables
3.3. Continuous random variables
3.4. Some discrete probability distributions.
3.4.1. Binomial distribution.
3.4.2. Poisson distribution.
3.4.3. Approximation of the Binomial distribution to the Poisson distribution.
3.5. Some continuous probability distributions.
3.5.1. Normal (or Gaussian) distribution. Definition, properties, use of the normal N (0.1) distribution table and applications.
3.5.2. Central Limit Theorem. Approximation of the Binomial distribution to the Normal distribution and approximation of the Poisson distribution to the distribution 2.5.3. Reference to other continuous distributions: Chi-square distribution, t-Student distribution and F-Snedcor distribution.
4. STATISTICAL ESTIMATION
4.1. Basic concepts: population and parameter; sample and statistics.
4.2. Point estimation of population parameters.
4.3. Interval estimation of population parameters.
5. PARAMETRIC HYPOTHESIS TESTS
5.1. Basic concepts: null hypothesis and alternative hypothesis, types of hypothesis tests (unilateral and bilateral), error typology, test statistics and critical region.
5.2. Proof value (p-value) of a hypothesis test. Conducting hypothesis tests using the p-value.
5.3. Most common parametric hypothesis tests.
6. SIMPLE LINEAR REGRESSION
6.1. Scatter diagram. Minimum squares method.
6.2.Pearson's linear correlation coefficient and determination coefficient.
6.3. ANOVA table.
Continuous assessment: 1st test rated from 0 to 5 values, 2nd test rated from 0 to 10 values and 3rd test rated from 0 to 5 values. The final grade will be the sum of the marks of the three tests, exempting the student from the exam, if it is equal to or higher than 9.5 values. Exam (from 0 to 20): written test, without consultation, on all subjects; the student will pass if it is equal to or higher than 9.5 values.
- Gama, S. e Pedrosa, A. (2016). Introdução Computacional à Probabilidade e Estatística, com Excel. Lisboa: Porto Editora
- Robalo, A. (1998). Estatística - Exercícios, Vol I (Probabilidades. Variáveis aleatórias). Lisboa: Edições Sílabo
- Robalo, A. (2004). Estatística - Exercícios, Vol II (Distribuições. Inferência Estatística) . Lisboa: Edições Sílabo
- Siegel, A. (1996). Statistics and Data Analysis: An Introduction. New York: John Wiley & Sons
Theoretical-practical classes with an expositive and practical component, with the proposal of exercises, promoting the active participation of students in their resolution. Emphasis is given software data analysis and results interpretation.
Software used in class