Probability and Statistics

Recommended Prerequisites

Mathematical Analysis I, Mathematical Analysis II

Teaching Methods

The teaching is provided in TP sessions. The lectures are expository and include examples that motivate the notions. Practical exercises are proposed and students must participate in solving them. As much as possible, examples and exercises in the area of Electrical and Computer Engineering are used.

Statistical models with computational means are used to increase the interpretation of results.

Weekly, tutorial time is offered.

There are 2 types of grading: during the semester, involving tests or midterm exams (100% weight), and by final examination, taking a written exam (100% weight). 

Learning Outcomes

The aim of the course is to introduce basic mathematical knowledge to prepare students to model the behavior of random phenomena that arise in the context of engineering. It contributes to prepare students to describe, analyze and interpret real situations using non-deterministic mathematical models. The correct use of statistical methods, and the strict interpretation of the results, requires a theoretical base in Probability and Statistics, present in this course.

It is also intended to prepare students for applying statistical methods and concepts to real situations of Engineering involving the estimation of parameters of a model, testing its fitness and to interpret, predict and decide on the phenomena under study.

Instrumental skills: analysis and synthesis, problem solving and decision-making capacity.

Personal skills: development of critical thinking, work in interdisciplinary teams, autonomous learning, adaptability to new situations and application of theoretical knowledge.

Work Placement(s)

No

Syllabus

Probability

Random experience, the space of outcomes, events.  Kolmogorov’ definition of probability. Conditional probability. Independence of events.

Random Variables and Distributions

Discrete and continuous real random variables. Moments. Order parameters. Principal discrete and continuous probabilistic models. Multidimensional distributions. Central limit theorem.

Parametric Estimation

Introduction to inferential statistics. Review of descriptive statistics. Point estimation: estimators, empirical mean and variance, point estimation methods. Interval estimation: confidence intervals, the method of the pivotal variable, applications (confidence intervals for the mean of a population, for the variance of a Gaussian population and for a proportion).

Hypothesis Tests

Parametric tests. Applications (test for the mean of a population, for the variance of a Gaussian population and for a proportion). 

Chi-square test of adjustment. 

Head Lecturer(s)

Maria Esmeralda Elvas Gonçalves

Assessment Methods

Final assessment
Exam: 100.0%

Continuous assessment
Frequency: 100.0%

Bibliography

GONÇALVES, E., E. NOGUEIRA, A.C. ROSA, Probabilidades e Estatística para Ciências e Tecnologia – Conceitos e exercícios resolvidos, 2016, Almedina.

Murteira, B., C. S. Ribeiro, J. A. Silva, C. Pimenta, Introdução à Estatística, 2010, 3ª ed., Escolar Editora, Lisboa.

Andrews, L.C., Phillips, R.L., Mathematical Techniques for Engineers and Scientists, 2003, Spie, Washington.

Devore, J. L., Probability and Statistics for Engineering and the Sciences, 2011, 8ª ed., Brooks/Cole.

Guimarães R., Sarsfield Cabral, J., Estatística, 2007, 2ª ed., McGraw-Hill, Lisboa.

Maroco, J., Estatística com utilização do SPSS, 2007, 3ª ed., Edições Sílabo.

Montgomery, D.C., G.C. Runger, Applied Statistics and Probability for Engineers, 4ª ed., 2007, Wiley.

Moore, D., McCabe, G., Introduction to the practice of statistics, 2011, Freeman, 7ª ed., New York