Introduction to Probability and Statistics

Code: MAT12619L

6 ECTS

Duration: 15 weeks/156 hours

Scientific Area: Mathematics

Teaching languages: Portuguese

Languages of tutoring support: Portuguese

Regime de Frequência: Presencial

Sustainable Development Goals

Educação de qualidade - Assegurar a educação inclusiva, e equitativa e de qualidade, e promover oportunidades de aprendizagem ao longo da vida para todos.

Trabalho digno e crescimento económico - Promover o crescimento económico sustentado, inclusivo e sustentável, emprego pleno e produtivo, e trabalho decente para todos.

Reduzir as desigualdades - Reduzir as desigualdades dentro dos países e entre eles.

Learning Goals

It is intended that students achieve the following learning outcomes in the course:
a) recover and consolidate basic knowledge of descriptive statistics and probability;
b) acquire knowledge about random variables and some theoretical probability distributions (discrete and continuous);
c) acquire knowledge and develop mathematical skills in the context of estimation (point and interval estimation) and decision-making ((non)parametric hypothesis tests);
d) acquire knowledge in studying the relationship between two variables (correlation and linear regression);
e) use the knowledge acquired and the skills developed to design and implement solutions to various applied problems, under conditions of uncertainty.

What is Statistics and its role in scientific work; population, sample. Descriptive statistics: graphical representation of data, sample characteristics. Probability: definitions, axiomatic and properties, conditional probability, Bayes' theorem. Discrete and continuous models. Discrete random pair. Central limit theorem. Statistical Inference: estimation by confidence intervals (for mean value, variance and difference of mean values of normal populations); hypothesis tests: on the mean value in normal populations and with large samples (t-tests); on variance in normal populations; for comparison of two populations, based on two independent samples and two paired samples (t-tests); non-parametric tests: fit and independence. Simple Linear Regression.

Teaching Methods

The teaching methodology consists of theoretical classes and practical laboratory classes. Theoretical classes are taught using slides projection, complemented by the presentation of topics on the board using application examples related to the course area. In practical laboratory classes, students will solve application exercises manually and using computational tools.

Assessment

The grades are within the interval [0,20]. Continuous assessment or by final exam, in accordance with the Academic Regulations of the University of Évora. The continuous assessment regime consists of two tests, with the same weight, with the minimum score, in each one, being 7 points. The final grade is the average of the frequencies. The exam assessment system requires the student to obtain a minimum grade of 9.5 (normal, appeal and special seasons).