2023
Introduction to Probability and Statistics
Name: Introduction to Probability and Statistics
Code: MAT12619L
6 ECTS
Duration: 15 weeks/156 hours
Scientific Area:
Mathematics
Teaching languages: Portuguese
Languages of tutoring support: Portuguese, English
Regime de Frequência: Presencial
Sustainable Development Goals
Learning Goals
It is intended that the student acquire the fundamental concepts of Probability and Statistics, which are an
indispensable tool for decision in situations of uncertainty, present in Engineering. In the end, they are
expected to be able to do a preliminary analysis of the data and make inferences about the parameters under study. Finally the simple linear regression model is presented, and students should know how to
adjust the least squares line, make tests and confidence intervals for the parameters and evaluate the quality of
adjustment.
This course unit is intended for students to acquire the ability to:
• individual and team work;
• use statistical software;
• analyze and treat a set of data, having the ability to choose the method
indispensable tool for decision in situations of uncertainty, present in Engineering. In the end, they are
expected to be able to do a preliminary analysis of the data and make inferences about the parameters under study. Finally the simple linear regression model is presented, and students should know how to
adjust the least squares line, make tests and confidence intervals for the parameters and evaluate the quality of
adjustment.
This course unit is intended for students to acquire the ability to:
• individual and team work;
• use statistical software;
• analyze and treat a set of data, having the ability to choose the method
Contents
What is Statistics and its role in scientific work; population, sample. Descriptive statistics: graphical representation of data, sample characteristics. Probability: definitions, axiomatic and properties, conditional probability, Bayes' theorem. Discrete and continuous models. Discrete random pair. Central limit theorem. Statistical Inference: estimation by confidence intervals (for mean value, variance and difference of mean values of normal populations); hypothesis tests: on the mean value in normal populations and with large samples (t-tests); on variance in normal populations; adjustment; on the mean value based on small samples and on non-normal populations (Wilcoxon and signal test); for comparison of two populations, based on two independent samples and two paired samples (t-tests, Mann-Whitney, Wilcoxon's and signs). Simple Linear Regression.
Teaching Methods
Theoretical classes will be taught using slide projections, complemented with the exposition of the subjects on the board. Theoretical contents will be illustrated with application examples related to the course area. In practical laboratory classes, students will solve application exercises using computational tools. In the evaluation of the discipline, the student can opt for continuous evaluation or exam. The continuous assessment regime consists of carrying out two frequencies (0-20), with the same weight, with a minimum score, in each, of 7 values. The final grade is the average of the frequencies. The assessment system by exam requires the student to obtain a minimum grade of 9.5 (normal, recourse and special seasons).
Students who so wish can do a computational work developed in the free software R, which increases the final grade of the evaluation by 20% as long as the grade of the work is greater than or equal to 8 values. The works must be discussed.
Students who so wish can do a computational work developed in the free software R, which increases the final grade of the evaluation by 20% as long as the grade of the work is greater than or equal to 8 values. The works must be discussed.
Teaching Staff
