Class Probabilities and Statistics

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

1. . Descriptive Statistics

Types of data: integers, continuous, categorical, arrays, matrices

Frequency tables  Measures of central tendency and variability

Visualization

2. Linear Regression

Independent vs. dependent variables. Scatter plots

Covariance and Pearson coefficient Regression line

Residuals, least squares method Calculating the estimate for the response given a certain value for the independent variable

3. Probability

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. Statistical Inference

Sample and random sample

Estimator and estimate for a proportion

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 40-minute tests and 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  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