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). (2h 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 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. (4h lectures)
Convergence criteria: in probability, almost sure, in r-mean and in distribution. Relations between different criteria.
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. Applications.
Chapter 10. Chi-square tests. (2h lectures)
The multinomial distribution and its normal approximation. Goodness-of-fit chi-square test.
Cao, R. y otros (2001). Introducción a la Estadística y sus aplicaciones. Ediciones Pirámide.
Fernández-Abascal, H. y otros (1995). Ejercicios de Cálculo de Probabilidades: resueltos y comentados. Ariel.
Peña, D. (2005). Fundamentos de Estadística. Alianza Editorial.
Quesada, V. y García, A. (1988). Lecciones de Cálculo de Probabilidades. Ediciones Díaz de Santos, S.A.
Vélez, R. (2004). Cálculo de probabilidades 2. Ediciones Académicas, S.A.
Vélez Ibarrola, R. y García Pérez, A. (1997). Principios de Inferencia Estadística. UNED.
Verzani, J. (2005). Using R for Introductory Statistics. Chapman and Hall.
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 based on continuous assessment and a final exam, where continuous assessment will contribute one half of the total assessment and the final exam will contribute the other half.
Continuous assessment will help to check competences CG3, CE1, CE7 and CE9 of the Degree in Mathematics.
Final exam will consist of a theoretical part and a practical part. The theoretical part will be based on concepts and short questions to assess whether some crucial knowledge is being acquired. The practical part will be focused on solving exercises and problems similar to those proposed and solved in seminars and labs.
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.
In the second opportunity of assessment, an exam will be done and the grade in this second opportunity will be a weighted average of the continuous assessment during the semester and the second opportunity exam, with weights 30% and 70%, respectively.
Continuous assessment will be adapted to the situation regarding COVID-19 as described below:
SCENARIO 1 (adapted normality). Continuous assessment will consist of problems individually solved by students and presented in seminars or through specific assignments in the virtual campus. Practical assignments will also be proposed, that can be done individually or in groups, in classrooms or by internet, using R software.
SCENARIO 2 (social distance). Continuous assessment will consist of problems, individually solved by students, and practical assignments using R, that can be in classrooms or by internet.
SCENARIO 3 (closing). Continuous assessment will consist of problems solved individually by students, and practical assignments using R. Activities that were expected to be in classrooms under scenarios 1 and 2 will be done by internet using MS Teams.
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
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.
Contingency plans for COVID-19:
SCENARIO 1 (adapted normality).
Teaching methodology: Lectures and interactive teaching will be given in classrooms, according to the plans of Facultad de Matemáticas, and will be supplemented with virtual campus (moodle), where students will find bibliographic materials, exercises, teaching videos, etc. Through the virtual campus, students will be able to make tests and to put their assignments for continuous assessment. Tutorial guidance will be in classrooms, by electronic mail or by MS Teams.
Continuous assessment: Continuous assessment will consist of problems individually solved by students and presented in seminars or through specific assignments in the virtual campus. Practical assignments will also be proposed, that can be done individually or in groups, in classrooms or by internet, using R software.
SCENARIO 2 (social distance).
Teaching methodology: Partially virtual teaching, according to the plans of Facultad de Matemáticas. Virtual campus (moodle) will be used, with teaching videos and bibliographic materials provided by professors, together with MS Teams platform. Tutorial guidance will be given by electronic mail or MS Teams.
Continuous assessment: Continuous assessment will consist of problems, individually solved by students, and practical assignments using R, that can be in classrooms or by internet.
SCENARIO 3 (closing).
Teaching methodology: Completely virtual teaching through the virtual campus (moodle), with some activities given by asynchronous materials. Tutorial guidance will be given by electronic mail or MS Teams.
Continuous assessment: Continuous assessment will consist of problems solved individually by students, and practical assignments using R. Activities that were expected to be in classrooms under scenarios 1 and 2 will be done by internet using MS Teams.
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
Coordinador/a- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- Phone
- 881813208
- cesar.sanchez [at] usc.es
- Category
- Professor: University Lecturer
Mercedes Conde Amboage
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- mercedes.amboage [at] usc.es
- Category
- Professor: LOU (Organic Law for Universities) PhD Assistant Professor
Laura Freijeiro González
- Department
- Statistics, Mathematical Analysis and Optimisation
- Area
- Statistics and Operations Research
- laura.freijeiro.gonzalez [at] usc.es
- Category
- Xunta Pre-doctoral Contract
| Monday | |||
|---|---|---|---|
| 10:00-11:00 | Grupo /CLE_01 | Spanish | Classroom 07 |
| 11:00-12:00 | Grupo /CLIL_01 | Spanish | Computer room 3 |
| 12:00-13:00 | Grupo /CLIL_03 | Galician, Spanish | Computer room 4 |
| 13:00-14:00 | Grupo /CLIL_02 | Galician, Spanish | Computer room 2 |
| Tuesday | |||
| 10:00-11:00 | Grupo /CLE_01 | Spanish | Classroom 09 |
| 11:00-12:00 | Grupo /CLIL_06 | Spanish | Computer room 4 |
| 12:00-13:00 | Grupo /CLIL_05 | Galician, Spanish | Computer room 3 |
| 13:00-14:00 | Grupo /CLIL_04 | Spanish, Galician | Computer room 2 |
| Wednesday | |||
| 09:00-10:00 | Grupo /CLIS_03 | Galician, Spanish | Classroom 03 |
| 10:00-11:00 | Grupo /CLIS_04 | Spanish, Galician | Graduation Hall |
| Thursday | |||
| 11:00-12:00 | Grupo /CLIS_01 | Spanish | Ramón María Aller Ulloa Main Hall |
| Friday | |||
| 13:00-14:00 | Grupo /CLIS_02 | Spanish | Classroom 03 |
| 01.14.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 02 |
| 01.14.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 03 |
| 01.14.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |
| 01.14.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 07 |
| 07.01.2021 16:00-20:00 | Grupo /CLE_01 | Classroom 06 |