Statistical Methods

Fundamental notions of set algebra, differential and integral calculus.

The teaching method is initially expository and inquisitive, with the introduction of concepts and techniques, accompanied by examples with application in the field of engineering, and then proceeds with the resolution of exercises by students, under the guidance of the teacher. The resolution of exercises using statistical functions of graphing calculators will be promoted. Whenever justified, computer tools (Excel) will also be used.

Objectives: Learn, understand and know how to use basic probability and statistical tools that allow the students exploring data and to analyze random models often used by practicing engineers.

Generic skills: Application of knowledge and understanding. Critical thinking. Interpretation of results. Communication. Self-learning. Ability to work in a group, developing interpersonal relationships.

Specific skills: Learn the main concepts of Probability and Statistics, for a follow-up and understanding of the topics to be addressed in this course, namely, learn and know how to use the methods of interpretation and data analysis, correlation and linear regression and the probabilistic models that constitute the bases of statistical inference. Learn to use and interpret basic statistical inference tools.

1. Descriptive Statistics. Basic notions. Descriptive statistics in one dimension: Frequency tables and graphical representation. Location measures and dispersion measures. Descriptive statistics in two dimensions: Contingency tables and dispersion diagrams. Covariance and correlation coefficient. Linear regression. Determination coefficient.

2. Introduction to Probability Theory. Introduction. Random experience, sample space, event. Probability definition. Properties. Conditional probability. Independent events. Total probability theorem. Bayes’ theorem.

3. Random Variables and Discrete Probability Distributions. Introduction. Discrete random variables: Definition; Probability function; Distribution function; Location and dispersion parameters. Special discrete distributions: Bernoulli, Binomial and Poisson.

4. Random Variables and Continuous Probability Distributions. Definition; Probability density function; Distribution function; Location and dispersion parameters. Special continuous distributions: Uniform, Exponential and Normal.

5. Introduction to Statistical Inference. Introduction. Brief introduction to sample design. Random sample. Sampling distributions. Point estimation. Fundamental notions of Interval Estimation. Confidence intervals for mean value  variance.

NAO

Main Bibliography:

Canova, F.  & Marques, M. . Apontamentos e exercícios de apoio às aulas. ISEC (available on academic platform  InforEstudante)

 Pedrosa, A. & Gama, S. (2018). Introdução Computacional à Probabilidade e Estatística com Excel (3ª ed.). Porto: Porto Editora. (ISEC library: 3-3-236)

Complementary Bibliography:

Ross, S.M. (2021). Introduction to Probability and Statistics for Engineers and Scientists (6th ed.). UK: Elsevier Inc.