The subject of STATISTICAL MATHEMATICS is a subject of the second semester of the second year and it has 6 ECTS. Classroom lessons are divided into three types: lectures (30 hours), classroom practices (15 hours) and computer practices (15 hours). In addition to the lessons, students will have to work 45 hours of lectures, 22.5 hours of classroom practice and 22.5 hours of computer practice.

Knowledge or Content:

RCO1: The graduate will be capable of identifying concepts and techniques from basic and specific subjects that allow the learning of new methods, theories, and modern engineering tools, providing sufficient versatility to adapt to new situations in their professional practice.

RCO5: The graduate will be able to identify concepts and methods related to mathematics that are applicable in the field of engineering.



Competencies:

RC4: The graduate will be capable of applying the strategies inherent to the scientific methodology: analyzing problematic situations both qualitatively and quantitatively, formulating hypotheses and solutions using models specific to renewable energy engineering.



Skills or Abilities:

HE1: The graduate will be capable of solving problems with initiative, decision-making, creativity, and critical reasoning.

HE5: The graduate will be capable of working effectively in a team constructively, integrating skills and knowledge to make decisions.

HE6: The graduate will be capable of acquiring new knowledge and skills for continuous learning, as well as pursuing further studies, with a high degree of autonomy.



Learning outcomes of the subject:

- Analyze and express ideas correctly using mathematical terminology.

- Statistically describe a sample by means of tables, graphs and measurements.

- Knows the concepts and applications of probability.

- Analyzes situations and models engineering problems of stochastic nature by means of variables

randomly.

- Correctly applies sampling and parameter estimation techniques.

- Applies basic regression models to engineering problems.

Unit 1 : Descriptive statistics.

Population and sample. Frequency distributions. Graphical representations and measurements.



Unit 2 : Combinatorial. Basic ideas of probability.

Variations, combinations and permutations. Random experiments. Algebra of events. Absolute and relative frequency of an event. Concept of probability. Axioms. Conditioned probability. Compound probability theorem. Dependent and independent events. Probability of the union of compatible events. Total probability theorem. Bayes' theorem.



Unit 3 : Discrete random variables.

Random variable. Classification. Discrete probability distributions. Probability function and distribution function. Mean and variance. Hypergeometric, binomial, geometric, negative binomial, Poisson and polynomial distribution.



Unit 4 : Continuous random variables.

Density function and distribution function. Mean and variance. Normal Gaussian distribution. Moivre's theorem. Pearson's chi-square distribution, Student's t and F by Fisher-Snedecor. Weibull distribution. Other distributions.



Unit 5 : Sampling and estimation theory.

Introduction. Means and variance of a linear combination of random variables. Central boundary theorem. Population and statistical sampling parameters. Parameter estimation. Fisher's theorem. Confidence interval of the mean and variance of a normal population. Confidence interval for the difference of means of two normal and independent populations. Confidence interval for the difference in means of two normal populations, paired samples. Variance ratio.



Unit 6 : Hypothesis contrast.

Introduction. Types of hypotheses. Type of contrasts. Type I and type II error. Critical region and region of acceptance. Contrasts on the mean and variance of a normal population. Contrasts on the difference of means of two normal and independent populations. Contrasts on the difference of means of two normal populations, paired samples.



Unit 7 : Analysis of variance.

Analysis of variance with one factor of variation and with two independent factors of variation Tables ANOVA and ANOVA II.



Unit 8: Regression and correlation.

Two-dimensional statistical variable. Scatter diagrams. Linear regression. Method of the least squares of Gauss. Correlation. Standard error of the estimation. Non-linear regression: Adjustment of exponential, potential and parabolic curves.

- Final exam: 75%. (It could be possible advance up to 15% throughout the course through activities)

- Computer training: 25%

A minimum score of 4 marks are required for both the computer training and the final exam.

• Continuous Assessment System
• Final Assessment System
• Tools and qualification percentages:
  • Written test to be taken (%): 75
  • Realization of Practical Work (exercises, cases or problems) (%): 25

In continuous evaluation the practices will be carried out throughout the four-month period and the written test on the day of the exam.



In the final evaluation the practices and the written test will be done on the day of the exam.



If classroom teaching should be replaced by virtual teaching, and above all, if it is not possible to take the exam in person, the assessment systems will be adapted to the situation. The tests taken so far (if any) will be kept. From then on, all the contents to be assessed will be evaluated by means of different tests and/or written and/or oral activities (papers, tests, exams, interviews...). As far as possible, the selected evaluation system will be maintained but continuous evaluation against the final will be encouraged.



Article 8.

In any case, students will have the right to be evaluated through the final assessment system, regardless of whether or not they have participated in the continuous or mixed assessment system. To do so, students must present a written waiver of continuous or mixed assessment to the teaching staff in charge of the subject, for which they will have a period of 9 weeks, counting from the beginning of the four-month period, in accordance with the school's academic calendar. In this case, the student will be evaluated with a single final exam, which will include a theoretical and practical part, and which will comprise 100% of the mark.



Article 12. Waiver of the call

12.2.- In the case of continuous evaluation, if the weight of the final test is higher than 40% of the grade of the course, it will be enough not to take the final test for the final grade of the course to be not submitted or presented. Otherwise, if the weight of the final test is equal to or less than 40% of the qualification of the subject, the students may waive the call within a period of at least one month before the end of the teaching period of the corresponding subject. This resignation must be presented in writing to the teaching staff responsible for the subject.

Article 9

The evaluation of the subjects in the extraordinary calls will be carried out exclusively through the final evaluation system.



The final assessment test of the extraordinary call will consist of as many tests and assessment activities as necessary to be able to assess and measure the defined learning outcomes, in a way that is comparable to how they were assessed in the ordinary call. The positive results obtained in each part by the students during the course may be kept.

Exercises notebook.

In the written test, a calculator and statistical tables may be used.

Basic bibliography

Probability and Statistics for Engineering and the Sciences. Jay L. Devore.

- NOVO SANJURJO V. Estadística Teórica y Aplicada. Ed. Sanz y Torres.

- NOVO SANJURJO V. Problemas de cálculo de probabilidades y estadística. Ed. Sanz y Torres

In-depth bibliography

GEORGE C. CANAVOS. Probabilidad y estadística. Aplicaciones y métodos. MacGraw -Hill

JOSE M. CASAS SANCHEZ. Inferencia estadística para economía y administración de empresas.
Ed. Centro de estudios Ramón Areces, S.A.

SIXTO RIOS. Análisis estadístico aplicado. Paraninfo.

KARMELE FERNANDEZ ETA BESTEAK. Estatistika-ariketak. Udako Euskal Unibertsitatea.

Journals

LA GACETA DE LA REAL SOCIEDAD MATEMATICA ESPAÑOLA

Web addresses

http://www.divulgamat.net
http://www.hiru.com
http://aulafacil.com/CursoEstadistica/CursoEstadistica.htm