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ISMAT 620

Probabilities and Statistics

Data Science
  • ApresentaçãoPresentation
    The curricular unit Probability and Statistics belongs to the scientific area of Statistics and provides the probabilistic and inferential foundations required for data analysis. It develops skills to model random phenomena, perform statistical inference and support data-driven decision making, constituting a fundamental curricular unit in Data Science.  
  • ProgramaProgramme
    S1: Probabilities Random experiences, space for results and events Definitions of probability and Kolmogorov axiomatic Bayes' theorem S2: Random Variables and Discrete Distributions Discrete random variables and their characteristics Discrete Uniform, Binomial, Poisson, Geometric and Hypergeometric Distributions S3: Random Variables and Continuous Distributions Continuous random variables and their characteristics Continuous Uniform, Normal and Exponential Distributions S4: Joint probability distributions and complements Joint, marginal and conditional distributions Covariance and correlation Central Limit Theorem S5: Estimation Introduction to Inferential Statistics Point and interval estimation S6: Hypothesis testing Parametric hypothesis tests Nonparametric hypothesis tests Normality and homoscedasticity S7: Simple Linear Regression models S8: Data Analysis using Software R  
  • ObjectivosObjectives
    At the end of this course unit, students should be able to: LO1: Distinguish concepts and solve problems involving probabilities; LO2: Characterize random variables and use them to solve problems; LO3: Build confidence intervals; LO4: Perform parametric hypothesis tests and verify their assumptions; LO5: Perform non-parametric hypothesis tests; LO6: Adjust, interpret and use simple linear regression models for predictive purposes; LO7: Use R software for statistical data analysis.  
  • BibliografiaBibliography
    Maindonald, J. & Braun, W. J. (2010). Data analysis and graphics using R: an example-based approach. (3rd ed.). United Kingdom: Cambridge University Press. Murteira, B. & Antunes, M. (2012). Probabilidades e Estatística. (Vol. 1). Lisboa: Escolar Editora.  
  • MetodologiaMethodology
    The teaching methodology includes the expository method (TM1) to present the contents, the demonstrative method (TM2) to illustrate its application to practical cases and the active method (TM3) to solve classroom exercises, with and without the use of a computer. Whenever appropriate, statistical software is used to explore concepts, interpret results and support the solution of real-world data analysis problems.  
  • LínguaLanguage
    Português
  • TipoType
    Semestral
  • ECTS
    8
  • NaturezaNature
    Mandatory
  • EstágioInternship
    Não