Description

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

Requirements

Subjects recommended to have taken before

• Mathematics: Linear Algebra — V05G301V01102
• Mathematics: Calculus 1 — V05G301V01101

Instructors

• Docampo Amoedo, Domingo
• Fernández Bernárdez, José Ramón
• Mojón Ojea, Artemio

Contents

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

Learning Outcomes

• B3 (CG3) – The knowledge of basic subjects and technologies that enables the student to learn new methods and technologies, giving them versatility to confront and adapt to new situations.
• B4 (CG4) – The ability to solve problems with initiative, make creative decisions, and communicate and transmit knowledge and skills, understanding the ethical and professional responsibility of the Technical Telecommunication Engineer.
• C1 (CE1/FB1) – The ability to solve mathematical problems in engineering, applying knowledge of linear algebra, geometry, differential geometry, differential and integral calculus, ordinary and partial differential equations, numerical methods, numerical algorithms, statistics and optimization.
• D2 (CT2) – Understanding engineering within a framework of sustainable development.
• D3 (CT3) – Awareness of the need for lifelong learning and continuous quality improvement, showing a flexible, open and ethical attitude toward different opinions and situations, particularly regarding non-discrimination based on sex, race or religion, and respect for fundamental rights and accessibility.

Recommended Readings and Tools

• Subjects that continue the syllabus
  • Data Communication — V05G301V01204
  • Computer Networks — V05G301V01210
  • Signal Transmission and Reception Techniques — V05G301V01208
  • Basics of Bioengineering — V05G301V01415
• Subjects recommended to be taken simultaneously
  • Mathematics: Calculus 2 — V05G301V01106

Planned Activities

• Lecturing – The course is divided into five main topics. Each topic includes a theoretical part presented by the teacher. Students are required to perform a prior reading of the corresponding contents.
  Competencies developed: CG3, CE1, CT3.
• Problem solving – Each topic is complemented with problem-solving sessions. Problems may be developed and solved in large or small group classes. Students are expected to work on these problems beforehand.
  Competencies developed: CG3, CG4, CE1, CT2, CT3.
• Practices through ICT – Each topic includes one or several computer practice sessions. A software tool developed by the teachers (based on Python) and specific questionnaires for each topic will be used. Students are required to read the relevant contents beforehand.
  Competencies developed: CG3, CG4, CE1, CT2, CT3.

Assessment Methods and Criteria

Evaluation Activities

• Problem and/or exercise solving – Students must solve a problem individually.
  Weight: 20%.
  Training and learning results: B3, B4, C1.
• Objective questions exam – Students must answer a multiple-choice test individually.
  Weight: 25%.
  Training and learning results: B3, B4, C1.
• Essay questions exam – Individual final exam.
  Weight: 40%.
  Training and learning results: B3, B4, C1.
• Essay – Individual submission of a problem solved independently.
  Weight: 15%.
  Training and learning results: B3, B4, C1.

Other Comments on the Evaluation

Following the guidelines of the degree programme, two evaluation systems are offered: continuous assessment and global assessment.

Each student may decide whether to follow continuous assessment. A student is considered to follow this system if they take Task 2 (around the seventh week of the term) or any subsequent task. Taking Task 1 alone does not imply commitment to continuous assessment. On the day of the final exam, students may still choose the global assessment system.

Continuous Assessment

Students who choose continuous assessment will complete several midterm tasks, each graded on a 0–10 scale. The final grade will be calculated as a weighted average of these tasks and the final exam.

The schedule of the midterm tasks will be approved by the Academic Committee of the Degree (CAG) and published at the beginning of the semester.

The tasks are:

• Task 1 (20%)
  Two parts with equal weight:
  • Part 1: Individual solution of a problem.
  • Part 2: Correction of a solution of the same problem prepared by another student.
• Task 2 (25%)
  Individual multiple-choice test.
• Task 3 (15%)
  Submission of a problem solved individually. Once the problem is assigned, it must be submitted within 48 hours.
• Final task (40%)
  Final exam, consisting of a reduced version of the exam taken by students choosing global assessment.

Before each task, the date and procedure for reviewing grades will be announced. Students will have the opportunity to review the correction of each task within approximately one week.

These tasks cannot be repeated if missed, except in cases of duly justified reasons.

During the course, additional exercises may be proposed during classes. Students following continuous assessment who complete these exercises may obtain a bonus of up to 0.5 points, which will be added to the final grade. If the resulting grade exceeds 10, the final grade will be 10.

Grades obtained in these tasks are valid only for the current academic year.

Students enrolled in continuous assessment who do not pass the course will receive a Fail, regardless of whether they take the final exam.

Global Assessment and End-of-Program Exam

Students choosing global assessment or taking the end-of-program examination will complete a single final exam covering the course contents. The exam is graded from 0 to 10, and the obtained score will be the student’s final grade.

Extraordinary Exam

The extraordinary exam is available only for students who have not passed the subject previously. Students may choose between continuous assessment or global assessment, regardless of the system chosen in the ordinary exam.

This choice must be indicated when handing in the exam. Grades will then be calculated according to the selected evaluation system as described above.

The course is considered passed when the final grade is equal to or greater than 5.

Academic Integrity

Plagiarism is considered serious academic misconduct. If plagiarism is detected in any test or assignment, the student will receive a final grade of 0 (Fail) and the incident will be reported to the appropriate academic authorities for disciplinary action.