Students will finish the class period with a maximum of 40% of the grade, achieved with the two written tests (10% each) and the two or three tests evaluating the laboratory practices (20%).On the date set by the Faculty in its annual program, students will perform, in writing, the final exam of the subject (60%), where they will have to answer theoretical questions, solve theoretical and practical issues, and calculate the solution of several problems. For this test, students will only bring the material expressly authorized (e.g. pen or calculator). The grade obtained in the final exam (60%) will be re-scaled so that students will have the opportunity to retrieve the 20% of the mark corresponding to the written controls (the 20% of the laboratory practice assessment mark cannot be retrieved). Thus, depending on the score obtained by the student in the two written controls, the highest score of the final exam will be between 6 and 8 points (out of 10). Thus, denoting by P the laboratory practice grade (between 0 and 2 points), denoting by C the written controls (Chapters 1 and 2) final grade (between 0 and 2 points) and denoting by F the final exam grade (between 0 and 10 points), the course final grade will be P+C+0'1*(8-C)*F. The day of the final exam, part-time students, who have not been previously evaluated for the laboratory practice part, will be able to perform a specific test to retrieve the 20% of the mark corresponding to that part.

Learning outcomes	Study programme competences
Have knowlegde about statistical techniques and knowing how to use them for the exploratory data analysis.	A1 A2 A3	B1 B5 B6	C1
Have knowlegde and understand the general concepts about probability models.	A1 A2 A3	B1 B5 B6	C1 C2
Knowing how to model in simple random contexts using probabilistic tools.	A1 A2 A3	B1 B5 B6	C1
Knowing how to use auxiliary computer tools for Statistics: statistical packages and programming languages with statistical orientation; and knowing how to critically interpret the results.	A1 A2 A3	B1 B5 B6	C1

Topic	Sub-topic
Probability	Definition of probability. Properties Conditional probability. Bayes’ theorem
Univariate random variables	Discrete random variables Continuous random variables Central limit theorem Applications: Reliability and simulation
Multivariate random variables	Bivariate discrete random variables Bivariate continuous random variables Marginal distributions Conditionated distributions Independent random variables Characteristic measures Multivariate random variables
Descriptive statistics	Frequency distributions Graphical representations Location and dispersion measures Two dimensional statistical variable Linear simple regression

Methodologies / tests	Competencies	Ordinary class hours	Student’s personal work hours	Total hours
Guest lecture / keynote speech	A1 A3 B5	30	48	78
Laboratory practice	C1	20	16	36
Seminar	A2 B6	10	10	20
Mixed objective/subjective test	B1	4	0	4

Personalized attention		12	0	12

(*)The information in the planning table is for guidance only and does not take into account the heterogeneity of the students.

Methodologies	Description
Guest lecture / keynote speech	Students will receive lectures where the professor, with the help of relevant audiovisual media, will present the theoretical and practical contents of the subject. Participation and debate will be encouraged at all times.
Laboratory practice	Laboratory practices will be held in a computer lab. It will be learned how to use the free statistical software R, and its programming structures. Statistical studies using both real and simulated data will be performed.
Seminar	Seminars will reinforce both the applied nature of the subject and its interactivity. Students will be able to express their doubts and concerns regarding the subject, and they will have the opportunity to perform, with the professor supervision, similar questions to those proposed in the exams. Additionally, with a very individualized attention, they will be able to complete the lab practices.
Mixed objective/subjective test	Students will have to show proficiency in the theoretical aspects of the subject and their ability to solve problems in the field of probability and statistics.

Methodologies	Competencies	Description	Qualification
Seminar	A2 B6	During the course, students will prove their interest in the subject and his mastery of it by performing two written tests (controls), each with a maximum mark of 10%. These two tests will correspond to Chapters 1 and 2 of the course. Students who do not obtain the maximum of 20% of the mark corresponding to this part will be able to retrieve the remaining part when taking the final exam of the subject.	20
Mixed objective/subjective test	B1	The final exam, with a value between 60% and 80% (depending on Chapters 1 and 2 written control grades), will consist of a theoretical and a practical written test.	60
Laboratory practice	C1	Students will develop lab practice exercises specifically designed to assess their monitoring of the subject. The correct completion of these exercises will be supervised by the professor in the classroom. To evaluate the degree of understanding and learning of these practices, 2 or 3 assessment tests will be scheduled. They will be performed during the laboratory classes having a 20% of the final grade. For enrolled full-time students, the practice mark is not retrievable by performing another test. Enrolled part-time students, who have not been evaluated of laboratory practices, may perform a specific test to retrieve the 20% of the mark corresponding to that part.	20

Assessment comments
<p>Students will finish the class period with a maximum of 40% of the grade, achieved with the two written tests (10% each) and the two or three tests evaluating the laboratory practices (20%).</p><p>On the date set by the Faculty in its annual program, students will perform, in writing, the final exam of the subject (60%), where they will have to answer theoretical questions, solve theoretical and practical issues, and calculate the solution of several problems. For this test, students will only bring the material expressly authorized (e.g. pen or calculator).<br /><br />The grade obtained in the final exam (60%) will be re-scaled so that students will have the opportunity to retrieve the 20% of the mark corresponding to the written controls (the 20% of the laboratory practice assessment mark cannot be retrieved). Thus, depending on the score obtained by the student in the two written controls, the highest score of the final exam will be between 6 and 8 points (out of 10). </p><p>Thus, denoting by P the laboratory practice grade (between 0 and 2 points), denoting by C the written controls (Chapters 1 and 2) final grade (between 0 and 2 points) and denoting by F the final exam grade (between 0 and 10 points), the course final grade will be P+C+0'1(8-C)F.<br /><br />The day of the final exam, part-time students, who have not been previously evaluated for the laboratory practice part, will be able to perform a specific test to retrieve the 20% of the mark corresponding to that part.</p><p><!--[if gte mso 9]><xml> <o:officedocumentsettings> <o:allowpng/> </o:officedocumentsettings> </xml> </body> </html> --></p>

Basic	Eguzkitza Arrizabalaga, J.M. (2014). Laboratorio de estadística y probabilidad con R. Gami Editorial Cao, R., Francisco, M., Naya, S., Presedo, M.A., Vázquez, M., Vilar, J.A. y Vilar, J.M. (2001). Introducción a la Estadística y sus aplicaciones. Ediciones Pirámide

Complementary	Gonick, L. y Smith, W. (2001). Á estatística ¡en caricaturas!. SGAPEIO R Development Core Team (2000). Introducción a R. http://www.r-project.org/ Blasco Lorenzo, A. y Pérez Díaz, S. (2015). Modelos aleatorios en ingeniería. Paraninfo Montgomery, D.C. y Runger, G.C. (2004). Probabilidad y Estadística aplicadas a la Ingeniería. McGraw-Hill Devore, J.L. (2008). Probabilidad y Estadística para Ingeniería y Ciencias. Thomson Walpole, R.E., Myers, S.L. y Myers, R. (2000). Probabilidad y Estadística para Ingenieríos. Prentice Hall Hernández, V., Ramos, E. y Yáñez, I. (2007). Probabilidad y sus aplicaciones en Ingeniería Informática. Ediciones Académicas Ugarte, M.D., Militino, A.F., Arnholt, A.T. (2008). Probability and Statistics with R. Chapman and Hall/CRC Horgan, J.M. (2009). Probability with R. An Introduction with Computer Science Applications. Wiley

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