Class Introduction to Mathematical Probability

The Probability and Statistics course aims to provide the student with fundamental concepts of of probability theory and techniques of descriptive statistics and statistical inference, essential for the study of Engineering.

Not applicable

1. Descriptive Statistics Types of data: integers, continuous, categorical… Frequency tables Measures of central tendency and dispersion Visualization (Bar charts, Histograms, Boxplots …)   2. Linear Regression Independent vs. Dependent variable Scatter plots Covariance and Pearson’s coefficient Regression line Residuals, least squares method Estimating the response given the value of the independent variable   3. Probability Theory Random experiment. Sample space. Event. Operations between events Properties of the probability function. Probability of the union of events Law of total probability. Bayes’ theorem Conditional probability. Independent events   4. Distributions Random variable Discrete distribution: Bernoulli Continuous distribution: Normal   5. Statistical Inference Sample and random sample Estimator and estimate for a proportion Confidence interval and hypothesis test for a proportion

Theoretical concepts are introduced in class, and then they are complemented with real-world examples. For each topic, the students are given a set of exercises that aim to apply the theoretical concepts. Exercises are discussed and solved in class, students are invited to share any doubts they might have.   Support materials and exercises with resolution suggestions will be available on Moodle.   It is believed that continuous assessment, adapted according to the evolution of students, is a good practice. Individual monitoring and availability to clarify doubts, whenever necessary, is essential for the student and his/her performance.

Apontamentos e séries de exercícios disponibilizados na plataforma moodle. Murteira, B. (2012), Probabilidades e Estatística, vols. I e II MacGraw-Hill. Murteira, B. (2007), Introdução à Estatística, MacGraw-Hill. Morais, M.C. (2020). Probabilidades e Estatística: Teoria, Exemplos & Exercícios. IST Press (Coleção Ensino da Ciência e da Tecnologia). Ross, S. M. (2014). Introduction to Probability and Statistics for Engineers and Scientists. 5th ed, Academic Press