Probability and Statistics

• Teachers
• Weekly hours
• Competences
• Objectives
• Contents
• Activities
• Teaching methodology
• Evaluation methodology
• Bibliography
• Web links
• Previous capacities

Teachers

Person in charge

• José Antonio González Alastrue ( )

Others

• Bhumika Ashvinbhai Patel ( )
• Erik Cobo Valeri ( )
• Jordi Cortés Martínez ( )
• Klaus Gerhard Langohr ( )
• Mireia Lopez Beltran ( )
• Nihan Acar Denizli ( )
• Nuria Perez Alvarez ( )
• Roser Rius Carrasco ( )

Weekly hours

Competences

Transversal Competences

Teamwork

• G5 - To be capable to work as a team member, being just one more member or performing management tasks, with the finality of contributing to develop projects in a pragmatic way and with responsibility sense; to assume compromises taking into account the available resources.
• CT3 - Ability to work as a member of an interdisciplinary team, as a normal member or performing direction tasks, in order to develop projects with pragmatism and sense of responsibility, making commitments taking into account the available resources.
• CTR3 - Capacity of being able to work as a team member, either as a regular member or performing directive activities, in order to help the development of projects in a pragmatic manner and with sense of responsibility; capability to take into account the available resources.

Entrepreneurship and innovation

• G1 - To know and understand the organization of a company and the sciences which govern its activity; capacity to understand the labour rules and the relation between planning, industrial and business strategies, quality and benefit. To develop creativity, entrepreneur spirit and innovation tendency.
• CT1 - Know and understand the organization of a company and the sciences that govern its activity; have the ability to understand labor standards and the relationships between planning, industrial and commercial strategies, quality and profit. Being aware of and understanding the mechanisms on which scientific research is based, as well as the mechanisms and instruments for transferring results among socio-economic agents involved in research, development and innovation processes.
• CTR1 - Capacity for knowing and understanding a business organization and the science that rules its activity, capability to understand the labour rules and the relationships between planning, industrial and commercial strategies, quality and profit. Capacity for developping creativity, entrepreneurship and innovation trend.

Appropiate attitude towards work

• G8 - To have motivation to be professional and to face new challenges, have a width vision of the possibilities of the career in the field of informatics engineering. To feel motivated for the quality and the continuous improvement, and behave rigorously in the professional development. Capacity to adapt oneself to organizational or technological changes. Capacity to work in situations with information shortage and/or time and/or resources restrictions.
• CT5 - Capability to be motivated for professional development, to meet new challenges and for continuous improvement. Capability to work in situations with lack of information.
• CTR5 - Capability to be motivated by professional achievement and to face new challenges, to have a broad vision of the possibilities of a career in the field of informatics engineering. Capability to be motivated by quality and continuous improvement, and to act strictly on professional development. Capability to adapt to technological or organizational changes. Capacity for working in absence of information and/or with time and/or resources constraints.

Reasoning

• G9 [Avaluable] - Capacity of critical, logical and mathematical reasoning. Capacity to solve problems in her study area. Abstraction capacity: capacity to create and use models that reflect real situations. Capacity to design and perform simple experiments and analyse and interpret its results. Analysis, synthesis and evaluation capacity.
  • G9.2 - Analysis and synthesis capacity, capacity to solve problems in its field, and to interpret the results in a critical way. Abstraction capacity: capacity to create and use models which reflect real situations. Capacity to design and perform simple experiments and to analyse and interpret their results in a critical way.
• CT6 - Capability to evaluate and analyze on a reasoned and critical way about situations, projects, proposals, reports and scientific-technical surveys. Capability to argue the reasons that explain or justify such situations, proposals, etc..
• CTR6 - Capacity for critical, logical and mathematical reasoning. Capability to solve problems in their area of study. Capacity for abstraction: the capability to create and use models that reflect real situations. Capability to design and implement simple experiments, and analyze and interpret their results. Capacity for analysis, synthesis and evaluation.

Sustainability and social commitment

• G2 - To know and understand the complexity of the economic and social phenomena typical of the welfare society. To be capable of analyse and evaluate the social and environmental impact.
• CT2 - Capability to know and understand the complexity of economic and social typical phenomena of the welfare society; capability to relate welfare with globalization and sustainability; capability to use technique, technology, economics and sustainability in a balanced and compatible way.
• CTR2 - Capability to know and understand the complexity of the typical economic and social phenomena of the welfare society. Capacity for being able to analyze and assess the social and environmental impact.

Third language

• G3 - To know the English language in a correct oral and written level, and accordingly to the needs of the graduates in Informatics Engineering. Capacity to work in a multidisciplinary group and in a multi-language environment and to communicate, orally and in a written way, knowledge, procedures, results and ideas related to the technical informatics engineer profession.
• CT5 - Achieving a level of spoken and written proficiency in a foreign language, preferably English, that meets the needs of the profession and the labour market.

Effective oral and written communication

• G4 - To communicate with other people knowledge, procedures, results and ideas orally and in a written way. To participate in discussions about topics related to the activity of a technical informatics engineer.

Information literacy

• G6 - To manage the acquisition, structuring, analysis and visualization of data and information of the field of the informatics engineering, and value in a critical way the results of this management.
• CT4 - Capacity for managing the acquisition, the structuring, analysis and visualization of data and information in the field of specialisation, and for critically assessing the results of this management.
• CTR4 - Capability to manage the acquisition, structuring, analysis and visualization of data and information in the area of informatics engineering, and critically assess the results of this effort.

Autonomous learning

• G7 - To detect deficiencies in the own knowledge and overcome them through critical reflection and choosing the best actuation to extend this knowledge. Capacity for learning new methods and technologies, and versatility to adapt oneself to new situations.

Analisis y sintesis

• CT7 - Capability to analyze and solve complex technical problems.

Basic

• CB6 - Ability to apply the acquired knowledge and capacity for solving problems in new or unknown environments within broader (or multidisciplinary) contexts related to their area of study.
• CB7 - Ability to integrate knowledge and handle the complexity of making judgments based on information which, being incomplete or limited, includes considerations on social and ethical responsibilities linked to the application of their knowledge and judgments.
• CB8 - Capability to communicate their conclusions, and the knowledge and rationale underpinning these, to both skilled and unskilled public in a clear and unambiguous way.
• CB9 - Possession of the learning skills that enable the students to continue studying in a way that will be mainly self-directed or autonomous.
• CB1 - That students have demonstrated to possess and understand knowledge in an area of ??study that starts from the base of general secondary education, and is usually found at a level that, although supported by advanced textbooks, also includes some aspects that imply Knowledge from the vanguard of their field of study.
• CB2 - That the students know how to apply their knowledge to their work or vocation in a professional way and possess the skills that are usually demonstrated through the elaboration and defense of arguments and problem solving within their area of ??study.
• CB3 - That students have the ability to gather and interpret relevant data (usually within their area of ??study) to make judgments that include a reflection on relevant social, scientific or ethical issues.
• CB4 - That the students can transmit information, ideas, problems and solutions to a specialized and non-specialized public.
• CB5 - That the students have developed those learning skills necessary to undertake later studies with a high degree of autonomy
• CB10 - Possess and understand knowledge that provides a basis or opportunity to be original in the development and/or application of ideas, often in a research context.

Transversals

• CT1 - Entrepreneurship and innovation. Know and understand the organization of a company and the sciences that govern its activity; Have the ability to understand labor standards and the relationships between planning, industrial and commercial strategies, quality and profit.
• CT2 - Sustainability and Social Commitment. To know and understand the complexity of economic and social phenomena typical of the welfare society; Be able to relate well-being to globalization and sustainability; Achieve skills to use in a balanced and compatible way the technique, the technology, the economy and the sustainability.
• CT3 - Efficient oral and written communication. Communicate in an oral and written way with other people about the results of learning, thinking and decision making; Participate in debates on topics of the specialty itself.
• CT4 - Teamwork. Be able to work as a member of an interdisciplinary team, either as a member or conducting management tasks, with the aim of contributing to develop projects with pragmatism and a sense of responsibility, taking commitments taking into account available resources.
• CT5 - Solvent use of information resources. Manage the acquisition, structuring, analysis and visualization of data and information in the field of specialty and critically evaluate the results of such management.
• CT6 - Autonomous Learning. Detect deficiencies in one's own knowledge and overcome them through critical reflection and the choice of the best action to extend this knowledge.
• CT7 - Third language. Know a third language, preferably English, with an adequate oral and written level and in line with the needs of graduates.

Gender perspective

• CT6 - An awareness and understanding of sexual and gender inequalities in society in relation to the field of the degree, and the incorporation of different needs and preferences due to sex and gender when designing solutions and solving problems.

Technical Competences

Common technical competencies

• CT1 - To demonstrate knowledge and comprehension of essential facts, concepts, principles and theories related to informatics and their disciplines of reference.
  • CT1.2A - To interpret, select and value concepts, theories, uses and technological developments related to computer science and its application derived from the needed fundamentals of mathematics, statistics and physics. Capacity to solve the mathematical problems presented in engineering. Talent to apply the knowledge about: algebra, differential and integral calculus and numeric methods; statistics and optimization.
• CT2 - To use properly theories, procedures and tools in the professional development of the informatics engineering in all its fields (specification, design, implementation, deployment and products evaluation) demonstrating the comprehension of the adopted compromises in the design decisions.
• CT3 - To demonstrate knowledge and comprehension of the organizational, economic and legal context where her work is developed (proper knowledge about the company concept, the institutional and legal framework of the company and its organization and management)
• CT4 - To demonstrate knowledge and capacity to apply the basic algorithmic procedures of the computer science technologies to design solutions for problems, analysing the suitability and complexity of the algorithms.
• CT5 - To analyse, design, build and maintain applications in a robust, secure and efficient way, choosing the most adequate paradigm and programming languages.
• CT6 - To demonstrate knowledge and comprehension about the internal operation of a computer and about the operation of communications between computers.
• CT7 - To evaluate and select hardware and software production platforms for executing applications and computer services.
• CT8 - To plan, conceive, deploy and manage computer projects, services and systems in every field, to lead the start-up, the continuous improvement and to value the economical and social impact.
  • CT8.3 - To demonstrate knowledge and be able to apply appropriate techniques for modelling and analysing different kinds of decisions.

Technical competencies

• CE1 - Skillfully use mathematical concepts and methods that underlie the problems of science and data engineering.
• CE2 - To be able to program solutions to engineering problems: Design efficient algorithmic solutions to a given computational problem, implement them in the form of a robust, structured and maintainable program, and check the validity of the solution.
• CE3 - Analyze complex phenomena through probability and statistics, and propose models of these types in specific situations. Formulate and solve mathematical optimization problems.
• CE4 - Use current computer systems, including high performance systems, for the process of large volumes of data from the knowledge of its structure, operation and particularities.
• CE5 - Design and apply techniques of signal processing, choosing between different technological tools, including those of Artificial vision, speech recognition and multimedia data processing.
• CE6 - Build or use systems of processing and comprehension of written language, integrating it into other systems driven by the data. Design systems for searching textual or hypertextual information and analysis of social networks.
• CE7 - Demonstrate knowledge and ability to apply the necessary tools for the storage, processing and access to data.
• CE8 - Ability to choose and employ techniques of statistical modeling and data analysis, evaluating the quality of the models, validating and interpreting them.
• CE9 - Ability to choose and employ a variety of automatic learning techniques and build systems that use them for decision making, even autonomously.
• CE10 - Visualization of information to facilitate the exploration and analysis of data, including the choice of adequate representation of these and the use of dimensionality reduction techniques.
• CE11 - Within the corporate context, understand the innovation process, be able to propose models and business plans based on data exploitation, analyze their feasibility and be able to communicate them convincingly.
• CE12 - Apply the project management practices in the integral management of the data exploitation engineering project that the student must carry out in the areas of scope, time, economic and risks.
• CE13 - (End-of-degree work) Plan and design and carry out projects of a professional nature in the field of data engineering, leading its implementation, continuous improvement and valuing its economic and social impact. Defend the project developed before a university court.

Especifics

• CE1 - Develop efficient algorithms based on the knowledge and understanding of the computational complexity theory and considering the main data structures within the scope of data science
• CE2 - Apply the fundamentals of data management and processing to a data science problem
• CE3 - Apply data integration methods to solve data science problems in heterogeneous data environments
• CE4 - Apply scalable storage and parallel data processing methods, including data streams, once the most appropriate methods for a data science problem have been identified
• CE5 - Model, design, and implement complex data systems, including data visualization
• CE6 - Design the Data Science process and apply scientific methodologies to obtain conclusions about populations and make decisions accordingly, from both structured and unstructured data and potentially stored in heterogeneous formats.
• CE7 - Identify the limitations imposed by data quality in a data science problem and apply techniques to smooth their impact
• CE8 - Extract information from structured and unstructured data by considering their multivariate nature.
• CE9 - Apply appropriate methods for the analysis of non-traditional data formats, such as processes and graphs, within the scope of data science
• CE10 - Identify machine learning and statistical modeling methods to use and apply them rigorously in order to solve a specific data science problem
• CE11 - Analyze and extract knowledge from unstructured information using natural language processing techniques, text and image mining
• CE12 - Apply data science in multidisciplinary projects to solve problems in new or poorly explored domains from a data science perspective that are economically viable, socially acceptable, and in accordance with current legislation
• CE13 - Identify the main threats related to ethics and data privacy in a data science project (both in terms of data management and analysis) and develop and implement appropriate measures to mitigate these threats
• CE14 - Execute, present and defend an original exercise carried out individually in front of an academic commission, consisting of an engineering project in the field of data science synthesizing the competences acquired in the studies

Technical Competences of each Specialization

Information systems specialization

• CSI2 - To integrate solutions of Information and Communication Technologies, and business processes to satisfy the information needs of the organizations, allowing them to achieve their objectives effectively.
• CSI3 - To determine the requirements of the information and communication systems of an organization, taking into account the aspects of security and compliance of the current normative and legislation.
• CSI4 - To participate actively in the specification, design, implementation and maintenance of the information and communication systems.
• CSI1 - To demonstrate comprehension and apply the principles and practices of the organization, in a way that they could link the technical and management communities of an organization, and participate actively in the user training.

Software engineering specialization

• CES1 - To develop, maintain and evaluate software services and systems which satisfy all user requirements, which behave reliably and efficiently, with a reasonable development and maintenance and which satisfy the rules for quality applying the theories, principles, methods and practices of Software Engineering.
• CES2 - To value the client needs and specify the software requirements to satisfy these needs, reconciling conflictive objectives through searching acceptable compromises, taking into account the limitations related to the cost, time, already developed systems and organizations.
• CES3 - To identify and analyse problems; design, develop, implement, verify and document software solutions having an adequate knowledge about the current theories, models and techniques.

Information technology specialization

• CTI1 - To define, plan and manage the installation of the ICT infrastructure of the organization.
• CTI2 - To guarantee that the ICT systems of an organization operate adequately, are secure and adequately installed, documented, personalized, maintained, updated and substituted, and the people of the organization receive a correct ICT support.
• CTI3 - To design solutions which integrate hardware, software and communication technologies (and capacity to develop specific solutions of systems software) for distributed systems and ubiquitous computation devices.
• CTI4 - To use methodologies centred on the user and the organization to develop, evaluate and manage applications and systems based on the information technologies which ensure the accessibility, ergonomics and usability of the systems.

Computer engineering specialization

• CEC1 - To design and build digital systems, including computers, systems based on microprocessors and communications systems.
• CEC2 - To analyse and evaluate computer architectures including parallel and distributed platforms, and develop and optimize software for these platforms.
• CEC3 - To develop and analyse hardware and software for embedded and/or very low consumption systems.
• CEC4 - To design, deploy, administrate and manage computer networks, and manage the guarantee and security of computer systems.

Computer science specialization

• CCO1 - To have an in-depth knowledge about the fundamental principles and computations models and be able to apply them to interpret, select, value, model and create new concepts, theories, uses and technological developments, related to informatics.
• CCO2 - To develop effectively and efficiently the adequate algorithms and software to solve complex computation problems.
• CCO3 - To develop computer solutions that, taking into account the execution environment and the computer architecture where they are executed, achieve the best performance.

Academic

• CEA1 - Capability to understand the basic principles of the Multiagent Systems operation main techniques , and to know how to use them in the environment of an intelligent service or system.
• CEA2 - Capability to understand the basic operation principles of Planning and Approximate Reasoning main techniques, and to know how to use in the environment of an intelligent system or service.
• CEA3 - Capability to understand the basic operation principles of Machine Learning main techniques, and to know how to use on the environment of an intelligent system or service.
• CEA4 - Capability to understand the basic operation principles of Computational Intelligence main techniques, and to know how to use in the environment of an intelligent system or service.
• CEA5 - Capability to understand the basic operation principles of Natural Language Processing main techniques, and to know how to use in the environment of an intelligent system or service.
• CEA6 - Capability to understand the basic operation principles of Computational Vision main techniques, and to know how to use in the environment of an intelligent system or service.
• CEA7 - Capability to understand the problems, and the solutions to problems in the professional practice of Artificial Intelligence application in business and industry environment.
• CEA8 - Capability to research in new techniques, methodologies, architectures, services or systems in the area of ??Artificial Intelligence.
• CEA9 - Capability to understand Multiagent Systems advanced techniques, and to know how to design, implement and apply these techniques in the development of intelligent applications, services or systems.
• CEA10 - Capability to understand advanced techniques of Human-Computer Interaction, and to know how to design, implement and apply these techniques in the development of intelligent applications, services or systems.
• CEA11 - Capability to understand the advanced techniques of Computational Intelligence, and to know how to design, implement and apply these techniques in the development of intelligent applications, services or systems.
• CEA12 - Capability to understand the advanced techniques of Knowledge Engineering, Machine Learning and Decision Support Systems, and to know how to design, implement and apply these techniques in the development of intelligent applications, services or systems.
• CEA13 - Capability to understand advanced techniques of Modeling , Reasoning and Problem Solving, and to know how to design, implement and apply these techniques in the development of intelligent applications, services or systems.
• CEA14 - Capability to understand the advanced techniques of Vision, Perception and Robotics, and to know how to design, implement and apply these techniques in the development of intelligent applications, services or systems.

Professional

• CEP1 - Capability to solve the analysis of information needs from different organizations, identifying the uncertainty and variability sources.
• CEP2 - Capability to solve the decision making problems from different organizations, integrating intelligent tools.
• CEP3 - Capacity for applying Artificial Intelligence techniques in technological and industrial environments to improve quality and productivity.
• CEP4 - Capability to design, write and report about computer science projects in the specific area of ??Artificial Intelligence.
• CEP5 - Capability to design new tools and new techniques of Artificial Intelligence in professional practice.
• CEP6 - Capability to assimilate and integrate the changing economic, social and technological environment to the objectives and procedures of informatic work in intelligent systems.
• CEP7 - Capability to respect the legal rules and deontology in professional practice.
• CEP8 - Capability to respect the surrounding environment and design and develop sustainable intelligent systems.

Direcció i gestió

• CDG1 - Capability to integrate technologies, applications, services and systems of Informatics Engineering, in general and in broader and multicisciplinary contexts.
• CDG2 - Capacity for strategic planning, development, direction, coordination, and technical and economic management in the areas of Informatics Engineering related to: systems, applications, services, networks, infrastructure or computer facilities and software development centers or factories, respecting the implementation of quality and environmental criteria in multidisciplinary working environments .
• CDG3 - Capability to manage research, development and innovation projects in companies and technology centers, guaranteeing the safety of people and assets, the final quality of products and their homologation.

Especifics

• CTE1 - Capability to model, design, define the architecture, implement, manage, operate, administrate and maintain applications, networks, systems, services and computer contents.
• CTE2 - Capability to understand and know how to apply the operation and organization of Internet, technologies and protocols for next generation networks, component models, middleware and services.
• CTE3 - Capability to secure, manage, audit and certify the quality of developments, processes, systems, services, applications and software products.
• CTE4 - Capability to design, develop, manage and evaluate mechanisms of certification and safety guarantee in the management and access to information in a local or distributed processing.
• CTE5 - Capability to analyze the information needs that arise in an environment and carry out all the stages in the process of building an information system.
• CTE6 - Capability to design and evaluate operating systems and servers, and applications and systems based on distributed computing.
• CTE7 - Capability to understand and to apply advanced knowledge of high performance computing and numerical or computational methods to engineering problems.
• CTE8 - Capability to design and develop systems, applications and services in embedded and ubiquitous systems .
• CTE9 - Capability to apply mathematical, statistical and artificial intelligence methods to model, design and develop applications, services, intelligent systems and knowledge-based systems.
• CTE10 - Capability to use and develop methodologies, methods, techniques, special-purpose programs, rules and standards for computer graphics.
• CTE11 - Capability to conceptualize, design, develop and evaluate human-computer interaction of products, systems, applications and informatic services.
• CTE12 - Capability to create and exploit virtual environments, and to the create, manageme and distribute of multimedia content.

Computer graphics and virtual reality

• CEE1.1 - Capability to understand and know how to apply current and future technologies for the design and evaluation of interactive graphic applications in three dimensions, either when priorizing image quality or when priorizing interactivity and speed, and to understand the associated commitments and the reasons that cause them.
• CEE1.2 - Capability to understand and know how to apply current and future technologies for the evaluation, implementation and operation of virtual and / or increased reality environments, and 3D user interfaces based on devices for natural interaction.
• CEE1.3 - Ability to integrate the technologies mentioned in CEE1.2 and CEE1.1 skills with other digital processing information technologies to build new applications as well as make significant contributions in multidisciplinary teams using computer graphics.

Computer networks and distributed systems

• CEE2.1 - Capability to understand models, problems and algorithms related to distributed systems, and to design and evaluate algorithms and systems that process the distribution problems and provide distributed services.
• CEE2.2 - Capability to understand models, problems and algorithms related to computer networks and to design and evaluate algorithms, protocols and systems that process the complexity of computer communications networks.
• CEE2.3 - Capability to understand models, problems and mathematical tools to analyze, design and evaluate computer networks and distributed systems.

Advanced computing

• CEE3.1 - Capability to identify computational barriers and to analyze the complexity of computational problems in different areas of science and technology as well as to represent high complexity problems in mathematical structures which can be treated effectively with algorithmic schemes.
• CEE3.2 - Capability to use a wide and varied spectrum of algorithmic resources to solve high difficulty algorithmic problems.
• CEE3.3 - Capability to understand the computational requirements of problems from non-informatics disciplines and to make significant contributions in multidisciplinary teams that use computing.

High performance computing

• CEE4.1 - Capability to analyze, evaluate and design computers and to propose new techniques for improvement in its architecture.
• CEE4.2 - Capability to analyze, evaluate, design and optimize software considering the architecture and to propose new optimization techniques.
• CEE4.3 - Capability to analyze, evaluate, design and manage system software in supercomputing environments.

Service engineering

• CEE5.1 - Capability to participate in improvement projects or to create service systems, providing in particular: a) innovation and research proposals based on new uses and developments of information technologies, b) application of the most appropriate software engineering and databases principles when developing information systems, c) definition, installation and management of infrastructure / platform necessary for the efficient running of service systems.
• CEE5.2 - Capability to apply obtained knowledge in any kind of service systems, being familiar with some of them, and thorough knowledge of eCommerce systems and their extensions (eBusiness, eOrganization, eGovernment, etc.).
• CEE5.3 - Capability to work in interdisciplinary engineering services teams and, provided the necessary domain experience, capability to work autonomously in specific service systems.

Specific

• CEC1 - Ability to apply scientific methodologies in the study and analysis of phenomena and systems in any field of Information Technology as well as in the conception, design and implementation of innovative and original computing solutions.
• CEC2 - Capacity for mathematical modelling, calculation and experimental design in engineering technology centres and business, particularly in research and innovation in all areas of Computer Science.
• CEC3 - Ability to apply innovative solutions and make progress in the knowledge that exploit the new paradigms of Informatics, particularly in distributed environments.

Generic Technical Competences

Generic

• CG1 - Identify and apply the most appropriate data management methods and processes to manage the data life cycle, considering both structured and unstructured data
• CG2 - Identify and apply methods of data analysis, knowledge extraction and visualization for data collected in disparate formats
• CG3 - Define, design and implement complex systems that cover all phases in data science projects
• CG4 - Design and implement data science projects in specific domains and in an innovative way
• CG5 - To be able to draw on fundamental knowledge and sound work methodologies acquired during the studies to adapt to the new technological scenarios of the future.
• CG6 - Capacity for general management, technical management and research projects management, development and innovation in companies and technology centers in the area of Computer Science.
• CG7 - Capacity for implementation, direction and management of computer manufacturing processes, with guarantee of safety for people and assets, the final quality of the products and their homologation.
• CG8 - Capability to apply the acquired knowledge and to solve problems in new or unfamiliar environments inside broad and multidisciplinary contexts, being able to integrate this knowledge.
• CG9 - Capacity to understand and apply ethical responsibility, law and professional deontology of the activity of the Informatics Engineering profession.
• CG10 - Capacity to apply economics, human resources and projects management principles, as well as legislation, regulation and standardization of Informatics.

Objectives

1. 2. Define and calculate probabilities for a random experience.
   Related competences: CT1.2A,
2. Calculate the conditional and joint probabilities and detect whether there is (in)dependence for a random experience with two variables and apply Bayes' theorem to locating the conditional probabilities for the other variable.
   Related competences: CT1.2A,
3. Graphically represent a random experience.
   Related competences: CT1.2A,
4. Calculate mean and variance for given probability and distribution functions for a discrete random variable.
   Related competences: CT1.2A,
5. Identify the most appropriate theoretical model to represent a given random variable from among the following: Bernoulli, binomial, Poisson, Geometric, Normal, uniform and exponential.
   Related competences: CT1.2A,
6. Calculate cumulative probabilities for certain values from the parameter for theoretical models with the help of tables or R; conversely, locate the random variable values from the desired cumulative probabilities.
   Related competences: CT1.2A, CT8.3, G9.2,
   Subcompetences:
   • They should also be able to identify and analyse theoretical models suitable for different IT situations.
7. Calculate and interpret the covariance and correlation values for two random variables.
   Related competences: CT1.2A,
8. Calculate, using sample data, statistics that reflect central tendency (mean) and dispersion (variance and standard deviation).
   Related competences: CT1.2A,
9. From sample indicators, obtained from a s.r.s., he/she will compute confidence intervals for certain parameters. For example: from the mean, the standard deviation and the sample size of a variable with Normal distribution, the student will calculate the CI95%.
   Related competences: CT1.2A,
10. Based on a hypothesis and the sample mean and standard deviation for a normally distributed variable, calculate the P-value and justify the evidence against the hypothesis.
    Related competences: CT1.2A, CT8.3,
11. From the data of a comparative test (e.g., performance of two computer products), the student will use the confidence interval to obtain a wide range of possible values of the difference in the outcome.
    Related competences: CT1.2A, CT8.3,
12. Using the summary of the model, obtain and interpret the estimators of the model, compute and interpret the R-squared coefficient, obtain the estimators of the uncertainty of the estimate and build a CI for the population values.
    Related competences: CT1.2A,
13. Make predictions and assess their degree of uncertainty using summary data from the adjusted model.
    Related competences: CT1.2A, CT8.3,
14. Based on the graphs of the adjusted model, analyze the premises of the model and, if necessary, propose transformations of the variables.
    Related competences: CT1.2A, CT8.3,
15. Design a prediction study, collect data and analyse and interpret results.
    Related competences: CT1.2A, CT8.3, G9.2,
    Subcompetences:
    • They should also be able to use the collected data to describe tendency and dispersion characteristics in numerical and graphical terms.
16. Identify, for a deterministic process, variability sources and magnitudes.
    Related competences: CT1.2A, CT8.3, G9.2,
    Subcompetences:
    • They should also be able to use collected data to describe tendency and dispersion characteristics in numerical and graphical terms.
17. Design a comparative test of computer products, collect data and analyse and interpret results.
    Related competences: CT1.2A, CT8.3, G9.2,
    Subcompetences:
    • They should also be able to use the collected data to describe tendency and dispersion characteristics in numerical and graphical terms.

Contents

1. Block A. Probability and random variables
   Random experiment. Probability, conditional probability, joint probability. Definition of random variable and types. Probability function, probability density function and probability distribution function. Joint probability function. Indicators: expectation, variance, standard deviation, covariance, correlation. Independence between two random variables.
2. Block B. Probabilistic models
   Parameterised theoretical models of random variables. Direct and inverse probabilities computation, with R. Introduction to simulation. Sample mean distribution. Central Limit Theorem, Normal approximations.
3. Block C. Basis of statistics
   Population and sample. Parameter, statistic and estimator. Bias of an estimator. Confidence interval for a parameter, and for the difference of two parameters. Hypothesis test
4. Block D. Statistical models and forecasting
   Comparació de dos grups, disseny aparellat, mostres independents. Model lineal. Indicadors de la qualitat de l'ajustament. Validació de les premisses. Introducció a la ciència de dades. Estudis experimentals i observacionals. Ètica de la ciència, research waste.
5. Block T. Application.
   Identifying sources of variability in computer processes. Design of a study with planning of the goal, data collection, statistical analysis with R and results interpretation.

Activities

Activity Evaluation act

Teaching methodology

Evaluation methodology

Bibliography

Basic:

• Estadística per a enginyers informàtics - González, J.A.; Cobo, E.; Muñoz, P.; Martí-Recober, M, Edicions UPC, 2008. ISBN: 9788483019535
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991003417199706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Probability and statistics for computer scientists - Baron, M, CRC Press, 2019. ISBN: 9781138044487
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991004181089706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Introducción a la estadística - Wonnacott, T.H.; Wonnacott, R.J, Limusa, 1997. ISBN: 9681845099
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991001638289706711&context=L&vid=34CSUC_UPC:VU1&lang=ca

Complementary:

• Probability with R: an introduction with computer science applications - Horgan, J.M, Wiley , 2009. ISBN: 9780470280737
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991003780759706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Estadística: modelos y métodos: vol.1: fundamentos - Peña, D, Alianza , 1986. ISBN: 8420689931
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991001319579706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• Probability models for computer science - Ross, S.M, Harcourt/Academic Press , 2002. ISBN: 9780125980517
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991003271789706711&context=L&vid=34CSUC_UPC:VU1&lang=ca
• From algorithms to Z-Scores: probabilistic and statistical modeling in computer science - Matloff, N.S, University Press of Florida , 2009. ISBN: 9781616100360
  https://discovery.upc.edu/discovery/fulldisplay?docid=alma991000807539706711&context=L&vid=34CSUC_UPC:VU1&lang=ca

Web links

• Servidor e-status https://estatus.upc.edu
• Pàgina web de Probabilitat i Estadística, amb material divers https://www-eio.upc.edu/teaching/pe/
• Repositori d'aplicatius shiny https://www-eio.upc.edu/~josean/shinyweb/jag_shiny.php

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