5 ECTS; 1º Ano, 2º Semestre, 60,0 TP , Cód. 203413.

**Lecturer**

- Francisco Paulo Vilhena Antunes Bernardino Carvalho (1)

- Maria Manuela Morgado Fernandes Oliveira (2)

(1) Docente Responsável

(2) Docente que lecciona

**Prerequisites**

Not applicable

**Objectives**

The Sustainable Development Goals (SDGs), SDGS4,SDS5 and SDS8 are considered fundamental in this Curricular Unit in a scenario of poverty eradication, environmental protection and the promotion of prosperity and well-being of all by 2030. They will be integrated into:

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 assessment: T1 (0-10 val.) + T2 (0-10 val.) mandatory and closed-book. If Students cumulatively, attain a score equal to or greater than 10

(rounding to units) are excused to the exam. Exam assessment: One written closed-book test.(minimum pass grade 10/20). At any time, students may be called to take a single and mandatory oral examination for clarification on the evaluation performed.

**Bibliography**

- Pedrosa, A. e Gama, S. (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 and practical classes including content presentation and illustrative cases of every topic in the syllabus, promoting and encouraging student participation in class discussion. Special emphasis is placed on economic data analysis.

**Software used in class**

Excel

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