Class Probabilities and Statistics

This subject is devoted to fundamental concepts in the theory of probability, statistics and statistical inference

Not applicable

1. Descriptive Statistics Types of data: integers, continuous, categorical… Frequency tables Measures of central tendency and dispersion Visualization (Bar charts, Histograms, Box plots...) 2. Linear Regression Independent vs. Dependent variable Scatter plots Covariance and Pearson’s coefficient Regression line Residual, least squares method Calculating the estimate of the response given a value for 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. Law of compound probability Conditional probability. Independent events 4. Distributions 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

In class, the ideas underlying the curriculum of this course are discussed, and multiple examples and application exercises are analyzed. For each topic in this course, a set of application exercises is presented. Students are encouraged to solve these exercises and to raise any doubts they may have. All supporting materials and relevant information will be shared with students through Moodle. The assessment includes a continuous component, which involves completing three 60-minute tests or a final exam (Final Exam or Make-up). The average of the three tests is denoted as A, and the Exam Grade is denoted as B. If A > 9.5, the student is approved for the course and can take the exam to improve the grade. In this case, the Final Grade = max(A, B). If A < 9.5, the student is not approved for the course and must take the exam to obtain approval. Students who achieve a final grade of at least 10 points are considered approved.

Morais, M. C. (2020): Probabilidades e Estatística: Teoria, Exemplos e Exercícios, IST Press (Coleção Ensino da Ciência e da Tecnologia) Murteira, B., Ribeiro, C.S., Andrade e Silva, J., e Pimenta C. (2010): Introdução à Estatística, Escolar Editora Murteira, B. (1993): Análise Exploratória de Dados - Estatística Descritiva, McGraw-Hill