The objective of the subject is to provide the basic principles of probability theory: random variables and probability distribution, and of statistical inference: parameter estimation and hypothesis testing.



The subject falls within the Basic Training module.



In this subject, knowledge gained in the following subjects is used:



- Calculus

- Algebra



The knowledge gained in this subject will be used in the following subjects:



- Business and Economics

- Fundamentals of Biomedical Signal Processing

- Biomedical Equipment

- Advanced Biomedical Signal Processing

- Biomedical Image Processing

GENERAL COMPETENCES

G003 - Knowledge in basic and technological subjects, which enable to learn new methods and theories, and provide versatility to adapt to new situations.



TRANSVERSAL COMPETENCES

T001 - Ability to solve problems with initiative, decision making, creativity and critical reasoning, respecting the principles of universal accessibility and design for all people.



SPECFIC COMPETENCES

M01FB01 - Ability to solve mathematical problems in engineering. Ability to apply knowledge of: linear algebra; geometry; differential geometry; differential and integral calculus; partial differential equations; differential equations; numerical methods; numerical algorithms; statistics and optimization.



LEARNING RESULTS

RAG5 - The graduate will be able to identify the concepts and methods related to mathematics that are applicable in the field of engineering.

RAT1 - The graduate will be able to solve problems with initiative, decision making, creativity and critical reasoning.

Topic 01. Descriptive Statistics. Measures of Central Tendency and Dispersion. Percentiles.

Topic 02. Probability.

Topic 03. Random variables.

Topic 04. Distribution models.

Topic 05. Statistical Inference: estimators, confidence intervals, hypothesis testing.

Topic 06. Regression and correlation.

The teaching methodology in this subject will be based on a combination of:



- Lectures: where the theoretical contents of the subject will be developed through the transmission of knowledge by the teacher in the classroom.



- Applied classroom-based groups: in this methodology the theoretical concepts of the subject will be applied to practical cases (exercises, problems, or case studies) that will be solved in the classroom.



- Computer lessons: in this methodology, students will be instructed in the use of MATLAB aiming to solve problems that require the application of theoretical-practical contents of the subject. In this methodology, which allows for small groups, the teacher will act as a guide and tutor in the process of solving and analyzing the proposed practical problems.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 70
  • Realization of Practical Work (exercises, cases or problems) (%): 30

Students might choose between continuous or final evaluation.



Continuous evaluation



1. The student's final score will be computed as the weighted sum of the grades obtained in the different tasks the student took part based on the following criteria:



- Final written exam: 50% of the final score



- Mid-term exam: 20% of the final score



- Practicum (exercises, cases or problems): 30% of the final score



2. To pass the subject it is mandatory to obtain at least 40% of the total score of the final written exam. If this minimum requirement is not met, the student might obtain a maximum final score of 4.5 and will be graded 'FAILED'.



3. The student, who want to drop out of the continuous evaluation in order to enroll in the final evaluation, will have to complete and sign an application form and deliver it to the lecturer before the 11th week of the semester. The application form will be available on the virtual platform 'egela'.



4. The fact of not taking the final written exam is considered equivalent to dropping out of the call and therefore, the student will be graded 'NOT PRESENTED'.





Final evaluation



1. The student must drop out of the continuous evaluation in order to enroll in the final evaluation. This must be done by completing and signing an application form and delivering it to the lecturer before the 11th week of the semester. The application form will be available on the virtual platform 'egela'.



2. The final evaluation consists of a final exercise composed of the following tasks:



- Final written exam: 70% of the final score



- Practicum (exercises, cases or problems): 30% of the final score



To pass the subject (final score >=5) the student must obtain at least 40% of the total score of the final written exam and 40% of the total score of the practicum. If this minimum requirement is not met, the student might obtain a maximum final score of 4.5 and will be graded 'FAILED'.



3. The fact of not taking the final written exam is considered equivalent to dropping out of the call and therefore, the student will be graded 'NOT PRESENTED'.

1. The score obtained during the semester in the continuous evaluation, i.e. that corresponding to the mid-term exam and practicum, will be maintained if it is greater or equal to 50% of its total; the student keeping that score will be evaluated according to the continuous evaluation and applying the same weights to each one of the tasks. To pass the subject it is mandatory to obtain at least 40% of the total score of the final written exam. If this minimum requirement is not met, the student might obtain a maximum final score of 4.5 and will be graded 'FAILED'.



2. The rest of the students will be evaluated according to the final evaluation system defined for the ordinary call.



To pass the subject (final score >=5) the student must obtain at least 40% of the total score of the final written exam and 40% of the total score of the practicum. If this minimum requirement is not met, the student might obtain a máximum final score of 4.5 and will be graded 'FAILED'.



3. The fact of not taking the final written exam is considered equivalent to dropping out of the call and therefore, the student will be graded 'NOT PRESENTED'.

Students are not forced to use any specific material.

Students might get all the necessary material to prepare and study the subject in the virtual platform 'egela'. This material will be make available as soon as the semester starts.

On the other hand, additional information can be obtained from the sources listed in the bibliography section of this document.

Basic bibliography

- A. P. King and R. J. Eckersley (2019): "Statistics for Biomedical Engineers and Scientists".

London: Academic Press.



- E. Aguirre (2006): "Estatistikaren oinarriak. Ariketak". Bilbao: Udako Euskal Unibertsitatea.



- G. Canavos (2001): "Probabilidad y Estadística. Aplicaciones y Métodos". México: McGraw-Hill.



- J.M. Eguzkitza (1999): "Apuntes de Métodos Estadísticos de la Ingeniería". Bilbao: Ed. Geneve.



- M.T. González y A. Pérez de Vargas Luque (2013): "Estadística Aplicada: Una visión instrumental". Madrid: Díez Santos, S.A.



- M.T. González (2021): "400 problemas resueltos de estadística multidisciplinar". Madrid: Díez Santos, S.A.



- W. Mendenhall y T. Sincich (1997): "Probabilidad y Estadística para Ingeniería y Ciencias". México: Prentice-Hall Hispano Americana, S.A.



- S.M. Ross (2005): "Introducción a la Estadística". Barcelona: Ed. Reverté.



- M.R. Spiegel (1991): "Estadística". Madrid: Ed. McGraw-Hill.

In-depth bibliography

- I. Bayo y J. M. Eguzkitza (2007): "Prácticas de Estadística con Mathematica". Bilbao: Servicio de Publicaciones EUITI.

- J. De la Horra Navarro (2003): "Estadística Aplicada". Madrid: Ed. Díaz de Santos.

- J. E. Freund, I. Miller y M. Miller (2000): "Estadística matemática con aplicaciones". México: Pearson Educación (Prentice Hall).

- J. M. García Pérez (1998): "Problemas resueltos de Estadística Básica". Madrid: Ed. UNED.

- V. Hernández, E. Ramos y R. Vélez (2011): "Modelos probabilísticos y optimización". Madrid: Ediciones Académicas S.A.

- V. Hernández, E. Ramos y I. Yáñez (2002): "Introducción al cálculo de probabilidades y sus aplicaciones a la ingeniería informática". Madrid: Ediciones Académicas S.A.

- W. Mendenhall y T. Sincich (1997): "Probabilidad y Estadística para Ingeniería y Ciencias". México: Prentice-Hall Hispano Americana, S.A.

- D. C. Montgomery y G. C. Runger (1999): "Applied Statistics and Probability for Engineers". Nueva York: John Wiley & Sons, Inc.

- E. Walpole, R. H. Myers y S. L. Myers (1999): "Probabilidad y estadística para ingenieros". México: Prentice Hall.

Web addresses

- OCW course: Statistics department (UC3M) - https://ocw.uc3m.es/course/index.php?categoryid=24

- OCW course on statistical methods via project-based learning (UPV/EHU) - https://ocw.ehu.eus/course/view.php?id=271

- OCW course on random variables (UPV/EHU) - https://ocw.ehu.eus/course/view.php?id=578

- OCW course on statistical analysis and inference using Mathematica (UPV/EHU) -
https://ocw.ehu.eus/course/view.php?id=506

- OCW course on statistical inference using R (UPV/EHU) - https://ocw.ehu.eus/course/view.php?id=580

- OCW course: Introduction to Probability and Statistics (MIT) - https://ocw.mit.edu/courses/mathematics/18-05-introduction-to-probability-and-statistics-spring-2014/