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 , Cód. 81429.
Lecturer
- Cristina Maria Mendes Andrade (1)(2)
(1) Docente Responsável
(2) Docente que lecciona
Prerequisites
Not applicable.
Objectives
1. Understand and be able to use the main concepts of:
1.1. Descriptive statistics.
1.2. Probability theory.
1.3. Random variables and probability distributions.
1.4. Estimation and hypothesis testing.
2. Proceed to data analysis, interpret the results and carry out a decision.
Program
1. DESCRIPTIVE STATISTICS
1.1. Importance and goals of Statistics. Data analysis method steps.
1.2. Characterization data.
1.3. Frequency distributions.
1.4. Measures of descriptive statistics
1.4.1. Measures of location: central tendency (mean, median and mode) and measures of position (quartiles, deciles and percentiles). Identification and classification of outliers. Box-plot.
1.4.2. Measures of dispersion.
1.4.3. Measures of skewness.
1.4.4. Measures of kurtosis.
2. PROBABILITY THEORY
2.1. Some notes on combinatorial analysis.
2.2. Definitions.
2.2.1. Random Experiments.
2.2.2. Probability space.
2.2.3. Events.
2.3. Properties of set theoretic operations.
2.4. Definition and properties of probability.
2.4.1. Classical definition of probability.
2.4.2. Relative frequency definition of probability.
2.4.3. Axioms of probability.
2.5. Conditional probability.
2.6. Independence events.
2.7. The law of total probability and the Bayes? Theorem.
3. RANDOM VARIABLES AND PROBABILITY DISTRIBUTIONS
3.1 Random variables.
3.1.1. Discrete random variables. Probability mass function and cumulative distribution function. Expected value, variance and some their properties. Mode and quartiles.
3.1.2. Continuous random variables. Probability density function and cumulative distribution function. Expected value, variance and some their properties. Mode and quartiles.
3.2. Some discrete probability distributions.
3.2.1. Binomial distribution.
3.2.2. Poisson?s distribution.
3.2.3. Poisson approximation to the Binomial distribution.
3.2.4. Other discrete probability distributions: geometric and hypergeometric.
3.3. Some continuous probability distributions
3.3.1. Normal distribution. Definition, properties, using the standardized Normal distribution N(0,1) table.
3.3.2. Central limit theorem. Normal approximation to the Binomial and Poisson?s distributions.
3.3.3. Other continuous probability distributions: Chi-square, Student?s t and Snedcor?s F distributions.
4. ESTIMATION
4.1. Basic concepts of estimation. Estimator and estimation.
4.2. Point estimation.
4.3. Interval estimation for the mean, proportion, variance and difference between means and variance.
5. PARAMETRIC HYPOTHESIS TESTS
5.1. Introduction to hypothesis tests. Null and alternative hypotheses, one-tailed and two-tailed hypothesis tests, types of errors, significance and power of hypothesis tests.
5.2. p-value method.
5.3 Hypothesis tests for various parameters.
6. Simple linear regression
6.1. Scatter Diagram. Least squares method.
6.2. Pearson's linear correlation coefficient and determination coefficient.
Evaluation Methodology
Continuous evaluation: 3 mandatory tests, 1st (0-5 values), 2nd (0-10 values) and 3rd (0-5 values). Final grade is the sum of the 3 tests.
Final written test (classification from 0 to 20) of all syllabus contents.
Approval in both evaluation periods: grade equal or superior to 10.
Bibliography
- 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
Teaching Method
Theoretical-practical lectures where beyond the theoretical exposition of the syllabus, practical applications of the topics presented are developed. Particular emphasis is placed on the analysis of economic data and management problems.
Software used in class
Excel.
