Probability and Statistics

Recommended Prerequisites

Mathematical Analysis I ,II.   

Teaching Methods

The teaching in this course assumes two formats: theoretical and example classes. During a theoretical class teaching is mostly expository. During an example class teaching consists of problem solving by the students under the guidance of the lecturer. A strong interaction between notions and their practical application is emphasized. In this task, the visualization and the analysis of concrete examples takes on a central role and prepares the way for the abstract definitions. Tutorial support is available to students to help them on the tasks assigned by the lecturers.

Learning Outcomes

The student who successfully completes this course will be able to:

1. Compute the probability of an event;

2. Model nondeterministic characteristics using random variables and their distributions;

3. Analyse samples and interpret the results;

4. Compute estimates for the mean and variance of a population and for a proportion;

5. Obtain the confidence intervals for the mean and variance of a population and for a proportion;

6. Design hypothesis tests for the mean and variance of a population and for a proportion;

7. Assess the compatibility of a sample with a statistical model using adjustment tests;

8. Use the notion of p-value in statistical software. 

Work Placement(s)

No

Syllabus

1. Probabilities: Kolmogorov probability definition and its consequences. Conditional probability. Independence of events.

2. Random variables and distributions: continuous and discrete real random variables. Discrete and continuous probabilistic models. Multidimensional distributions. Central Limit Theorem and applications.

3. Point and interval estimation of parameters.

4. Hypothesis tests: Parametric tests. Adjustment tests. Independence tests.

Head Lecturer(s)

Maria Esmeralda Elvas Gonçalves

Assessment Methods

Continuous assessment
2 or more midterm exams: 100.0%

Final assessment
Exam: 100.0%

Bibliography

[1] Gonçalves, E., E. Nogueira, A.C. Rosa, Probabilidades e Estatística para Ciências e Tecnologia – Conceitos e exercícios resolvidos, 2016, Edições Almedina, SA, Coimbra.

[2] Murteira, B., C. S. Ribeiro, J. A. Silva, C. Pimenta, F. Pimenta, Introdução à Estatística, 2015, 3 ed., Escolar Editora, Lisboa.

[3] Andrews, L.C., R. L. Phillips, Mathematical Techniques for Engineers and Scientists, 2003, Spie, Washington.

[4] Devore, J. L., Probability and Statistics for Engineering and the Sciences, 2016, 9 ed., Cengage Learning, Boston.

[5] Guimarães R., J. Sarsfield Cabral, Estatística, 2010, 2 ed., Verlag Dashofer Portugal, Lisboa.

[6] Maroco, J., Análise estatística com o SPSS Statistics, 2018, 7 ed., Report Number.

[7] Montgomery, D.C., G.C. Runger, Applied Statistics and Probability for Engineers, 4 ed., 2007, Wiley.