Elements of Probability and Statistics

To introduce the students in the tools of the Descriptive Data Analysis and the Theory of Probability. To learn introductory R language fundamentals and basic syntax for introductory statistics.

Descriptive statistics for one variable (4 lecture hours).
Introduction to descriptive statistics. Types of data and variables.
Frequencies. Measures of location, dispersion and shape.
Graphic tools of descriptive analysis of one variable.

Two-dimensional descriptive statistics (5 lecture hours).
Joint distribution of frequencies. Tables. Marginal and conditional frequencies.
Graphic tools for two variables.
Linear dependence. Regression lines. Covariance and correlation.

Probability Calculus (7 lecture hours).
Probability space. Events. Probability. Properties.
Conditional probability. Independence. Law of total probability. Bayes' theorem.
Combinatorics

One-dimensional random variables (5 lecture hours).
Random variable. Distribution function. Types of random variables: Discrete and continuous. Mass probability function and density function.
Characteristics of a random variable. Transformation of random variables.

Main models of probability (7 lecture hours).
Discrete: Uniform, Bernoulli, Binomial, Poisson, Hipergeometric, Geometric, Negative Binomial.
Continuous: Uniform, Normal, Exponential, Gamma, Beta.
Relations of interest between the distributions.

Contents of the laboratory classes (14 laboratory hours).
The statistica package R.
Exploratory data analysis.
Generation of probability models with R.

Basic bibliography:
- FREEDMAN, D. et al.(2011). Statistics. Fourth edition. Viva Books. (2nd edition in spanish: Estadística. Antoni Bosch, 1993).
- PEÑA, D. (2008). Fundamentos de Estadística. Segunda edición. Ciencias Sociales Alianza Editorial.
- TIJMS, H. C. (2016). Understanding Probability. Third edition. Cambridge University Press.

Complementary bibliography:
- CAO, R. et al. (2006). Introducción a la Estadística y sus aplicaciones. Ciencia y técnica (Pirámide).
- GONICK, L., SMITH, W. (2001). Á Estadística ¡en caricaturas!. Published by SGAPEIO.
- GRINSTEAD, C. M., SNELL, J. L. (1997). Introduction to Probability. Second edition. AMS.
- ROHATGI, V. K., EHSANES SALEH, A. K. Md. (2015) An Introduction to Probability and Statistics. Wiley Online Library. (Available online through the University Library).
- VERZANI, J. (2005). Using R for Introductory Statistics. Chapman and Hall.

According to the document "Memoria do Grao en Matemáticas da USC", competences that should be acquired across this course are:

Basic competencies: CB1-CB5
General competencies: CG1-CG5
Transversal competencies: CT1-CT5
Specific competencies: CE1-CE9

Lectures will consist, basically, in lessons given by the lecturer dedicated to the exposition of theoretical contents and the resolution of problems or exercises. Competences that should be acquired across this lectures are: CB1-CB4, CG1-CG4, CT3, CT5, CE1-CE7.

During the problem sessions, students will develop their capacity to solve exercises related to the concepts described in the theory classes. Competences that should be acquired across this sessions are: CB1-CB4, CG1-CG4, CT1-CT5, CE1-CE7.

The lab sessions will serve for the acquisition of practical skills and the illustration of theoretical contents. Competences that should be acquired across this sessions are: CB1-CB4, CG1-CG4, CT1-CT5, CE1-CE9.

In preparing the final exam and the partial evaluations, students will develop competences CB1-CB5, CG1-CG5, CT1-CT5, CE1-CE7.

All the tasks of the student will be oriented by the teacher in the tutorial sessions.

The material for this course will be available through the Virtual campus of the USC. Also, communications with the students will be carried out through this platform. The material for this course will be available through the Virtual campus of the USC. Also, communications with the students will be carried out through this platform. MS Teams will be used as a synchronous communication tool. Depending on the healthcare scenario in which the teaching will be develope, the methodology will be adapted as follows:

The expository and interactive teaching will be on classroom, using the virtual course as support, in which the students will find bibliographic and teaching materials, together with problem bulletins. The tutorials will be in person or through MS Teams.

The final grade (FG) will be the highest between the final exam score (FE) and the weighted average of this score with the continuous evaluation score (CE), where the relative weight of each section will be 70%-30%, respectively.

FG=max{FE,0.7*FE+0.3*CE}

The continuous evaluation will consist of solving problems and questions that will be periodically programmed in the corresponding seminar/lab sessions. The number of continuous assessment tests will be the same in all interactive teaching groups, with a similar format. Three tests will be scheduled throughout the course, which will always be done with the available class material. The teacher will comment on the tasks in the following sessions. The continuous evaluation grade will be the average of the scores of the established activities.

The final exam is the same in all expository teaching groups. It will consist of a section based on short questions intended to evaluate the acquisition of key knowledge in the subject. The rest of the exam will consist of solving exercises and problems similar to those proposed throughout the course.

It will be understood as "Not presented" those who does not take the final exam.

In the second opportunity, the continuous evaluation grades and grading criteria will be maintained.

The assessment of competencies is carried out according to the methodology established in the teaching section.

The total number of working hours of the student is: 25 x 6 = 150. The distribution is as follows:

PRESENCE WORK IN THE CLASSROOM
Lectures classes: 26 hours
Solving-problems laboratory classes: 13 hours
Computer laboratory classes: 13 hours
Small groups tutorials: 2 hours
Total: 54 hours

HOURS OF PERSONAL WORK OF THE STUDENT
Individual and group self-study: 74 hours
Preparation of continuous assessment tests: 7 hours
Programming and other works with computer: 15 hours
Total: 96 hours

It is recommended to attend lectures and seminars and to do the suggested activities. It is also recommended the use of the R statistical package for exploring the practical usefulness of the techniques explained along the course.

The software R that will be used in laboratory sessions can be freely downloaded from http://www.r-project.org.

Warning. In cases of fraudulent performance of exercises or tests (plagiarism or improper use of technologies), the provisions of the Regulations for the Evaluation of the Academic Performance of students and the revision of qualifications will apply.