ECTS credits ECTS credits: 6
ECTS Hours Rules/Memories Student's work ECTS: 99 Hours of tutorials: 3 Expository Class: 24 Interactive Classroom: 24 Total: 150
Use languages Spanish, Galician
Type: Ordinary Degree Subject RD 1393/2007 - 822/2021
Departments: Statistics, Mathematical Analysis and Optimisation
Areas: Statistics and Operations Research
Center Faculty of Mathematics
Call: First Semester
Teaching: With teaching
Enrolment: Enrollable
The objectives of this course are that the students:
- Know the concepts and basic operations with a random vector.
- Understand the basic elements of Statistical Inference.
- Use the concepts and applications of Asymptotic Theory.
These objectives are an indispensable tool in Statistics, and will be required in the courses “Statistical Inference” and “Regression models and multivariate analysis”.
Chapter 1. Basic elements in a random vector. (3h lectures)
Concept of random vector. Discrete and continuous random vectors. Joint, marginal and conditioned distributions. Independence of random variables. Change of variable in random vectors.
Chapter 2. Mean vector and covariance matrix. (2h lectures)
Concepts of mean vector and covariance matrix. Linear operations on random vectors. Standardization.
Chapter 3. The multivariate normal distribution. (3h lectures)
Definition of the multivariate normal distribution. Linear operations on multivariate normal vectors. Standardization. The chi-square distribution. Quadratic operations on a sample of normal observations.
Chapter 4. Estimation and confidence intervals (Proportions and normal populations). (3h lectures)
Introduction to Statistical Inference. Parameter estimation. Confidence intervals for a proportion and the mean and variance of a normal population.
Chapter 5. Hypothesis testing (Proportions and normal populations). (3h lectures)
Introduction to the problem of hypothesis testing. Null and alternative hypotheses. Decision errors, significance level and power. Testing hypotheses about the proportion and the mean and variance of a normal population. The p-value.
Chapter 6. Two-sample problem. (2h lectures)
Two-sample Student’s T test, with paired samples and independent samples. Testing two variances. Testing two proportions.
Chapter 7. Moment-generating function and characteristic function. (3h lectures)
Moment-generating function: definition, properties and applications. Characteristic function: definition, properties and applications. Reproductivity of distribution models.
Chapter 8. Convergence of sequences of random variables. (5h lectures)
Convergence criteria: in probability, almost sure, in r-mean and in distribution. Relations between different criteria. Properties, continuous mapping theorem and Slutsky’s theorem.
Chapter 9. Law of large numbers and central limit theorem. (4h lectures)
Weak laws of large numbers. Strong laws of large numbers. Central limit theorem. The delta method. Applications of limit theorems to Statistics.
BASIC BIBLIOGRAPHY:
Vélez Ibarrola, R. (2004). Cálculo de probabilidades 2. Ediciones Académicas, S.A. (online access through BUSC https://prelo.usc.es/Record/Xebook1-7234)
Vélez Ibarrola, R. and García Pérez, A. (1997). Principios de Inferencia Estadística. UNED.
COMPLEMENTARY BIBLIOGRAPHY:
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…
Cao, R. et al. (2001). Introducción a la Estadística y sus aplicaciones. Ediciones Pirámide.
Fernández-Abascal, H. et al. (1995). Ejercicios de Cálculo de Probabilidades: resueltos y comentados. Ariel.
Peña, D. (2005). Fundamentos de Estadística. Alianza Editorial.
Quesada, V. and García, A. (1988). Lecciones de Cálculo de Probabilidades. Ediciones Díaz de Santos, S.A.
Verzani, J. (2014). Using R for Introductory Statistics. Chapman and Hall. (online access through https://www.taylorfrancis.com/books/mono/10.1201/9781315373089/using-in…)
In this course, according to the proposal for the Degree in Mathematics, the following competences will be enhanced: basic competences with the codes CB3 and CB4, general competences with the codes CG2 and CG3, cross-area competences with the codes CT1, CT3 and CT5, and specific competences with the codes CE1, CE2, CE5 and CE9.
The course will comprise lectures, interactive seminars, interactive computer labs and tutorial guidance in small groups.
During the lectures, the professors will introduce theoretical concepts illustrated with problems and exercises.
During the interactive seminars, exercises previously proposed by the professors will be solved by the students, who will prepare the solutions in advance to the sessions. Then, exercises will be corrected during the interactive sessions.
Interactive computer labs will be devoted to learning R software to implement the statistical methods of this course.
Tutorial guidance in small groups will be used to guide the learning process and to solve doubts.
Assessment will be the maximum of the final examen and the weighted average of the final exam and continuous assessment, where continuous assessment will contribute on 35% and the final exam on 65%. The assessment system will be the same in first and second opportunities, keeping the continuous assesment also for the second opportunity.
The final exam will contain questions on concepts or short issues in which the acquisition of key knowledge of the subject is intended to be assessed, together with exercises and practical problems similar to those proposed throughout the course, which may contain elements of the R statistical package used in the laboratory classes.
Continuous assessment will weight 35% of the total assessment and will be composed of 15% corresponding to a written exam in the middle of the semester, 5% coming from the students’ participation in seminars, and 15% from the evaluations made in computer labs, that will be carried out by means of one or two written quiz at the labs.
Both the continuous assessment tests and the final exam will be identical in all the lecture and interactive teaching groups of the subject.
Competence CB4 will be checked in seminar labs and competence CE9 in computer labs. All other competences will be checked through the rest of evaluation systems in continuous asessment and the final exam
Evaluation attendance: a student will be considered as attending the evaluation when he/she has participated in any evaluation activity, either in continuous assessment or in the final exam.
Individual work is about one hour and a half for each hour of teaching, including preparation of the assignments and study of R software.
Attending lectures, seminars, computer labs and tutorial guidance is strongly recommended as fundamental tools to follow the course. Solving proposed exercises, studying the topics in a timely manner and practising R software are useful habits to get a fruitful outcome from the course.
R software, which will be the basic tool in computer labs, can be freely downloaded from http://www.r-project.org/
Online moodle-based platform “Campus Virtual” will be used.
For cases of fraudulent performance of exercises or tests will apply the provisions of the "Normativa de avaliación do rendemento académico dos/das estudantes e de revisión de cualificacións".
This guide and the criteria and methodologies described in it are subject to modifications derived from regulations and guidelines of the USC.
Wenceslao Gonzalez Manteiga
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813204
- wenceslao.gonzalez [at] usc.es
- Category
- Professor: University Professor
Cesar Andres Sanchez Sellero
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813208
- cesar.sanchez [at] usc.es
- Category
- Professor: University Lecturer
Maria Isabel Borrajo Garcia
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- mariaisabel.borrajo [at] usc.es
- Category
- Professor: Temporary PhD professor
Ignacio Gomez Casares
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813391
- ignaciogomez.casares [at] usc.es
- Category
- Ministry Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLIL_05 | Spanish, Galician | Computer room 2 |
| 11:00-12:00 | Grupo /CLE_01 | Spanish | Classroom 06 |
| 11:00-12:00 | Grupo /CLIL_06 | Galician, Spanish | Computer room 2 |
| 13:00-14:00 | Grupo /CLIL_04 | Galician, Spanish | Computer room 2 |
| Tuesday | |||
| 10:00-11:00 | Grupo /CLIS_01 | Spanish | Classroom 03 |
| 11:00-12:00 | Grupo /CLE_02 | Spanish, Galician | Classroom 06 |
| Wednesday | |||
| 09:00-10:00 | Grupo /CLE_02 | Galician, Spanish | Classroom 06 |
| 10:00-11:00 | Grupo /CLE_01 | Spanish | Classroom 02 |
| 11:00-12:00 | Grupo /CLIL_01 | Spanish | Computer room 4 |
| 12:00-13:00 | Grupo /CLIL_02 | Spanish | Computer room 3 |
| 13:00-14:00 | Grupo /CLIL_03 | Spanish | Computer room 3 |
| Thursday | |||
| 09:00-10:00 | Grupo /CLIS_03 | Galician, Spanish | Classroom 06 |
| 10:00-11:00 | Grupo /CLIS_04 | Galician, Spanish | Classroom 02 |
| Friday | |||
| 10:00-11:00 | Grupo /CLIS_02 | Spanish | Classroom 03 |
| 01.20.2025 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 06.16.2025 10:00-14:00 | Grupo /CLE_01 | Classroom 06 |