Mathematics: Probability and Statistics

About this course

The aim of this subject is to study some basic concepts of statistics, probability and random processes. These concepts are necessary in order to easily follow other subsequent subjects.

Expected learning outcomes

Knowledge of basic subjects and technologies that enables the student to learn new methods and technologies, as well as to give him great versatility to confront and adapt to new situations

Ability to solve problems with initiative, to make creative decisions and to communicate and transmit knowledge and skills, understanding the ethical and professional responsibility of the Technical Telecommunication Engineer activity.

Ability to solve mathematical problems in Engineering. The aptitude to apply knowledge about linear algebra, geometry, differential geometry, differential and integral calculus, differential and partial differential equations; numerical methods, numerical algorithms, statistics and optimization

Understanding Engineering within a framework of sustainable development.

Awareness of the need for long-life training and continuous quality improvement, showing a flexible, open and ethical attitude toward different opinions and situations, particularly on non-discrimination based on sex, race or religion, as well as respect for fundamental rights, accessibility, etc.

Indicative Syllabus

Probability theory
– Concept of probability.
– Axiomatic definition.
– Conditional probability, total probability and Bayes theorems.
– Independence.
One-dimensional random variables
– Concept of random variable (RV). Classification.
– Cumulative distribution function (CDF) and properties.
– Discrete random variables: probability mass function.
– Continuous random varriables: density function.
– Functions of an RV. CDF and discrete RV.
– Transformation of continuous RVs: fundamental theorem.
– Mean and variance.
Random vectors
– CFD and continuous RV.
– Marginals. Point and line masses.
– Conditional density. Continuous versions of Bayes and total probability theorems.
– Functions of two-dimensional RVs: fundamental theorem.
– Changes of dimension.
– Correlation and regression.
Estimation and limit theorems
– Sample and population.
– Estimators.
– Estimation of mean and variance.
– Sequences of RVs. Laws of large numbers.
– Central limit theorem.
Stochastic processes
– Description of a stochastic process.
– Statistics of a stochastic process.
– Stationarity.
– Examples.

Teaching / Learning Methodology

28hrs of lecturing + 14hrs of practices through ICT + 1hr of problem and/or exercise solving + 3hrs of tests + 87hrs of student autonomous work

Recommended Reading

TBA