Statistics

The main goal of this course is to make the students familiar with the basic concepts and techniques of Descriptive Statistics, Probability and Statistical Inference, especially applied to the Coomputer Engineering field.

UNIT 1. DESCRIPTIVE STATISTICS
1.1 General concepts.
1.2 Frequency distributions.
1.3 Graphic representations.
1.4 Characteristic measurements: position, dispersion, and shape.
1.5 Bidimensional descriptive statistics. Contingency tables, scatter plot and linear regression.

UNIT 2. PROBABILITY FOUNDATIONS
2.1 Random experiment. Events and sample space.
2.2 Assignment and definition of probability. Operations with events.
2.3 Conditional probability. Independence of events. Remarkable results.

UNIT 3. DISCREET RANDOM VARIABLE
3.1 Discrete variable. Support, probability mass function and distribution function.
3.2 Characteristic measures.
3.3 Main models of discrete distributions.

UNIT 4. CONTINUOUS RANDOM VARIABLE
4.1 Continuous variable. Density function and distribution function.
4.2 Characteristic measures.
4.3 Main models of continuous distributions.
4.4 Central Limit Theorem.
4.4 Approximation of distributions.

UNIT 5. INTRODUCTION TO STATISTICAL INFERENCE AND ESTIMATION OF PARAMETERS
5.1 Introduction to Statistical Inference.
5.2 Estimation for one population.
5.3 Estimation for two populations
5.4 Estimation by confidence intervals.

UNIT 6. CONTRAST OF HYPOTHESIS
6.1 Introduction to hypothesis testing.
6.2 Contrast procedure.
6.3 Contrasts for one population.
6.4 Contrasts for two populations.

CONTENTS OF THE PRACTICES WITH A COMPUTER: introduction to R; descriptive statistics; simple linear regression; random variables; distributions in sampling; confidence intervals and hypothesis testing.

BASIC BIBLIOGRAPHY
Borrajo, M. I. et al. (2020): Estatística Descritiva. Colección Esenciais USC. https://www.usc.gal/libros/gl/categorias/948-estatistica-descritiva-334…
Borrajo, M. I. et al. (2021): Fundamentos da Teoría da Probabilidade. Colección Esenciais USC. https://www.usc.gal/libros/gl/categorias/1025-fundamentos-da-teoria-da-…
Borrajo, M. I. et al. (2021): O programa estatístico R. Colección Esenciais USC. https://www.usc.gal/libros/gl/categorias/1024-o-programa-estatistico-r-…
Borrajo, M. I. et al. (2023): Inferencia Estatística Paramétrica I. Colección Esenciais USC. https://www.usc.gal/libros/gl/categorias/1183-inferencia-estatistica-pa…
Borrajo, M. I. et al. (2023): Inferencia Estatística Paramétrica II. Colección Esenciais USC. https://www.usc.gal/libros/gl/categorias/1182-inferencia-estatistica-pa…
Febrero Bande, M., Galeano San Miguel, P., González Díaz, J. and Pateiro López, B. (2008). Estadística: ingeniería técnica en informática de sistemas. Universidade de Santiago de Compostela, Santiago de Compostela.
Fernández-Viagas, Escudero, V., Framiñán Torres, J. M., Pérez González, P. and Villa Caro, G. (2016) Problemas resueltos de probabilidad y estadística en la ingeniería. Universidad de Sevilla, Sevilla.
Montgomery, D. C., Runger, G. C. and Medal, E. G. U. (2007). Probabilidad y estadística aplicadas a la ingeniería. Limusa-Wiley, México.
Peña, D. (1993). Estadística: Modelos y Métodos. Alianza Editorial, Madrid.
Verzani, J. (2005). Using R for Introductory Statistics. Chapman and Hall.

FURTHER READING
Cao, R., Francisco, M., Naya, S., Presedo, M. A., Vázquez, M., Vilar, J. A. and Vilar, J. M. (1998). Estadística básica aplicada. Tórculo Edicións, Santiago de Compostela.
Cao, R., Francisco, M., Naya, S., Presedo, M. A., Vázquez, M., Vilar, J. A. and Vilar, J. M. (2001). Introducción a la Estadística y sus aplicaciones. Ediciones Pirámide, Madrid.
Devore, J. L. (2001). Probabilidad y Estadística para Ingeniería y Ciencias. Thomson Learnin, México.
Guisande-González, C., Vaamonde-Liste, A. and Barreiro-Felpeto, A. (2011). Tratamiento de datos con R, Statistica y SPSS. Díaz de Santos, Madrid.
Mendenhall, W. M. and Sincich, T. L. (2016). Statistics for Engineering and the Sciences. CRC Press, Boca Raton.
Peña, D. (1991). Fundamentos de estadística. Alianza Editorial, Madrid.
Quesada Paloma, V. and García Pérez, A. (1988). Lecciones de cálculo de probabilidades. Ediciones Díaz de Santos, Madrid.
Ross, S. M. (2014). Introduction to probability and statistics for engineers and scientists. Elsevier, Burlington.

All the recommended basic bibliography is available at the Escola de Enxeñaría library. The complementary bibliography can be found in the libraries of the Universidade de Santiago de Compostela, where there is also a notable bibliographic collection on statistics and manuals for the use of statistical software.

After taking this course, students are expected to work on the skills listed in the report of the Degree in Computer Science Engineering of the Universidade de Santiago de Compostela. Thus, students must acquire the following basic, general, and transversal skills: CB1, CB3, CB4, CB5, CG5, CG8, CG9, CG10, TR1, TR2, TR3, FB1, FB3, RI6 and TI5.

As learning outcomes, a basic knowledge is provided for the treatment, management and summary of the information using statistical methods. To do this, the fundamentals of statistics are introduced at a descriptive level to then establish the bases of the probability theory on which the statistical modelling of random variables is based.

After this first introductory phase, this knowledge is applied to interesting problems of inference and linear models that have to do with prediction, quality control and efficient decision making. Among other examples applied to the field of computer engineering, they will be seen: how to study the useful life of a piece of a computer, how to calculate the recommended capacity of a server according to the number of users who enter a web page, how to verify if a piece tends to be more defective than the manufacturer claims, how to check if a brand offers computers that are more durable on average than another.

In the sections containing the methodology and the evaluation system, we describe the way in which the competencies (general, transversal, basic, of the branch of computer science and information technology) are worked on and evaluated. In the case of the specific competences of the mathematics module and specific to the subject, all the training activities to be developed aim to work on these competences.

Expository teaching (25 hours). For the transmission of knowledge, use will be made of slides and blackboard and standard problems will be solved, so that students can work on the provided exercise bulletins. Regarding the material for the follow-up of the subject, beyond the recommended bibliography, the students will have the help of additional material in the Virtual Campus of the USC. In the expository teaching sessions, the following skills will be worked on: basic skills (CB1 and CB5), general (CG8 and CG9), transversal (TR2, TR3, FB3 and RI6).

Practices with computer (14 hours). For this type of teaching, the free statistical software R will be used. Outside the classroom, students will have to practice the use of R independently to consolidate concepts and face the problems of analysing databases and programming functions on their own. For the follow-up of the sessions in the computer room, the scripts of the practices will be provided to students. Developed objectives: basic skills (CB3, CB4 and CB5), general (CG5) and transversal (TR1, FB1, RI6 and TI5).

Problem-solving sessions (10 hours). In these seminar sessións, the involvement of students in solving practical exercises will be guided by the teacher. Developed objectives: basic skills (CB1, CB3 and CB5), general (CG9 and CG10) and transversal (TR1, TR2, FB1 and FB3).

Tutorials (3 hours): the tutorials are intended to monitor student learning. In the tutoring sessions, different activities will be carried out that allow students to achieve an overview of the subject and, at the same time, identify in which aspects they should improve. Developed objectives: basic skills (CB1, CB3, CB4 and CB5) and transversal (TR1 and TR2).

The distribution of the hours of expository teaching (25 hours) and problem-solving seminars (10 hours), by topic, is as follows, in one-hour sessions:
Unit 1. Descriptive statistics. (5 lectures, 2 seminars).
Unit 2. Fundamentals of probability. (4 lectures, 1 seminar).
Unit 3. Discrete random variables. (4 lectures, 1 seminar).
Unit 4. Continuous random variables. (4 lectures, 2 seminars).
Unit 5. Introduction to Inference and parameter estimation. (4 lectures, 2 seminars).
Unit 6. Hypothesis testing. (4 lectures, 2 seminars).

The interactive teaching in the laboratory (14 hours) is divided into 7 practices, the contents of which are linked to various topics. As a guideline, the distribution of practices is as follows:
Practice 1. Introduction to R. (2 hours)
Practice 2. Descriptive statistics. (2 hours, Unit 1)
Practice 3. Random variables (2 hours, Unit 3, Unit 4)
Practice 4. Regression (2 hours, Unit 1, Unit 4)
Practice 5. Sampling distributions (2 hours, Unit 5)
Practice 6. Confidence intervals and hypothesis testing (2 hours, Unit 5, Unit 6)
Practice 7. Assesment. (2 hours).

During the course, the degree to which the students have achieved the proposed objectives for this subject will be continuously evaluated. Ending with a practical theoretical exam. The weight of each part of the evaluation is detailed below.

Continuous evaluation (30%): continuous evaluation will be carried out based on participation in different types of tasks. The continuous evaluation activities will include the resolution of practical cases (individually or in groups), which may include the use of the statistical software R. Individual resolution exercises will also be proposed to be carried out in and/or not in person. The grade obtained will be kept between opportunities in the same academic year (ordinary and extraordinary). During this part, the participation and involvement of the students in the classroom will also be evaluated. To qualify for this part, whenever possible, it is necessary to attend at least 75% of the practical sessions. Students who have already met this requirement in at least one of the last two academic years will be exempt from this condition, after notifying the teaching staff. Evaluated competences: CB1, CB3, CB4, CB5, CG5, CG8, CG9, CG10, TR1, TR2, TR3, FB1 and FB3.

Final exam (70%): the final exam will consist of several questions and theoretical-practical exercises on the contents of the subject, within which the interpretation of results obtained with the statistical package used in interactive teaching may be included. Evaluated competences: CB1, CB3, CB5, CG9, CG10, TR3, FB1, FB3, RI6, RI6 and TI5.

Note that, in cases of fraudulent performance of the exam or tests, the provisions of the "Regulations for the evaluation of the academic performance of students and the review of grades" ("Normativa de avaliación do rendemento académico dos estudantes e de revisión de cualificacións" in Galician) will apply.

Finally, it is considered that the evaluation is not attended when the student does not participate in any scoring activity. The weight of the continuous evaluation in the second opportunity will be the same as in the ordinary call for the semester.

In this subject, the students have the following teaching given by the professors: 25 hours of expository teaching, 14 hours of computer practice and 10 hours of problem-solving. Besides that, the students will have to dedicate 52 hours to deepen the knowledge of the lectures, 20 hours for the computer sessions and 15 for the problem-solving. During these hours, the acquired knowledge should be deepened, through the revision of concepts, practice of problem solving and the consultation of the recommended bibliography.

The follow-up to the expository and interactive sessions is essential to overcome the subject. Students must carry out all the activities recommended by the teaching staff (problem solving, bibliography review and practical exercises) to successfully pass the subject. In addition, it is recommended to make use of the tutorial hours to resolve any questions that may arise.

Subject specific teaching material will be posted at the Virtual Campus.

This guide and the criteria and methods described therein are subject to changes arising from regulations and guidelines USC.