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Class Probabilities and Statistics

  • Presentation

    Presentation

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

  • Code

    Code

    ULHT2531-15
  • Syllabus

    Syllabus

    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

  • Objectives

    Objectives

    This subject aims to show that

    LG1: probability is as an essential measure function in science.

    LG2: statistics enables us to collect data, analyse data, establish hypothesis on data and test these hypothesis. Hence, both probability and statistics lead us to knowledge in science and engineering

  • Teaching methodologies and assessment

    Teaching methodologies and assessment

    • 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 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.
  • References

    References

    • 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
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