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.

Evaluation can be periodic or by final exam.

  Periodic evaluation (to schedule in due course):

• Test 1: theoretical-practical, covering material from chapters 1 to 3, quoted at 10.0 points;
• Test 2: theoretical-practical, covering material from chapters 4 and 5, quoted at 10.0 points.

        Requires that the classification obtained in each test is greater than or equal to 3.5 values ​​(out of 10).

• The student is approved by periodic evaluation if the sum of the marks obtained in the two tests is greater than or equal to 9.5 points and meets the minimum requirements. 
• It is assumed that the student chooses the periodic evaluation, which replaces the 1st exam period, when taking Test 1.
• If the student did not obtain the minimums in Test 2, and only in Test 2, he/she may take a corresponding test at the 2nd exam period.

  Evaluation by final exam:

   Exam, theoretical-practical, quoted for 20 points, to perform during exam periods. The student is approved if he/she obtains a grade greater than or         equal to 9.5 points.

Academic Fraud: The current IPC regulations will be applied to all situations of attempted or consummated academic fraud.

NAO