Class Introduction to Mathematical Probability

  • Presentation


    The Introduction to Mathematical Probability 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 Data Science.


  • Code


  • Syllabus


    1. Descriptive Statistics:

    • Frequency tables;
    • Graphic representation;
    • Sample measures of location and dispersion;


    2. Linear Regression:

    • Estimate the model parameters;
    • Calculate and understand the coefficient of determination;


    3. Probability Theory: 

    • Sample space; Events;
    • Algebra of events and properties: Concepts of probability, Axiomatic of Kolmogorov, Properties of probability function;
    • Conditioned Probability: Independence; Bayes theorem;


    4. Discrete and continuous random variables:

    • Probability function, Probability density function and Distribution function;
    • Parameters of random variables: Mean, Variance and Standard deviation;


    5. Discrete distributions: Bernoulli, Binomial and Poisson;


    6. Continuous distributions: Normal and Exponential;


    7. Statistical Inference:

    • Sample and Random Sample. Sample mean;


    8. Estimation:

    • Confidence Intervals for Expected Value;
    • Hypothesis Tests for Expected Value.
  • Objectives


    We expect students can:


    • Be able to organize statistical data and perform descriptive statistical analysis and understand the main statistical measures of location and dispersion;
    • Understand the essential theoretical aspects of linear regression models.
    • Understand the fundamental concepts of probability theory and know how to calculate the probabilities associated with the phenomenon under study;
    • Be able to characterize random variables and identify their probability distributions;
    • Be able to apply appropriate point and interval estimation techniques to infer the characteristics of a population based on a sample and analyze the results obtained;
    • Understand the general procedures for applying a hypothesis test;
    • Understand the probability and statistics as an area of science that allows o collect and analyze data, formulate hypotheses regarding that data, and test those hypotheses. 
  • Teaching methodologies and assessment

    Teaching methodologies and assessment

    Theoretical concepts are introduced in class, and then they are complemented with practical 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.

  • References


    • 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.


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