Statistical Methods for Engineering

Objectives

• Know the main theoretical models used to model phenomena that contain uncertainty.
• Study the fundamentals of probability necessary to build these models.
• Study the main one-dimensional probability distributions.
• Study the concept of one-dimensional random variable.
• Know probability calculation techniques related with random variables.
• Know the concept of two-dimensional random variables, and the concept of independence of two random variables.
• Know the statistical tools of confidence intervals and hypothesis testing.
• Use confidence intervals and/or hypothesis testing to take decisions based on statistics.
• Know the fundamentals of linear regression and its main indicators.
• Know statistical techniques applied to quality control.
• Work with computer packages for statistical modelling (Programming Lab).

Learning outcomes

• To explain the basic concepts of probability and statistics. (1)
• To analytically and numerically solve problems of probability and statistics. (2, 3)
• To identify and use the terminology, notation and methods of probability and statistics. (4)
• To critically analyse the results obtained. (5)
• To efficiently use ICT for virtual interaction. (6)
• To collect and interpret data and information on which to base conclusions, including, when appropriate, reflections on matters of a social, scientific or ethical nature in their field of study. (7)

Competencies

General skills

• Act professionally, with ethical commitment and respect for criteria of sustainability, accessibility and universal design.
• Combine scientific knowledge with technical skills and technological resources to deal with problems in professional practice.

Specific skills

• Understand basic mathematical theory to solve mathematical problems that can arise in engineering and apply knowledge about linear algebra; geometry; differential geometry, differential and integral calculus; ordinary differential equations and partial differential equations; numerical methods; numerical algorithms, statistics and optimisation.

Basic skills

• Students can apply their knowledge to their work or vocation in a professional manner and have competencies typically demonstrated through drafting and defending arguments and solving problems in their field of study.
• Students have demonstrated knowledge and understanding in a field of study that builds on general secondary education with the support of advanced textbooks and knowledge of the latest advances in this field of study.
• Students have the ability to gather and interpret relevant data (usually within their field of study) in order to make judgements that include reflection on relevant social, scientific and ethical issues.

Core skills

• Be a critical thinker before knowledge in all its dimensions. Show intellectual, cultural and scientific curiosity and a commitment to professional rigour and quality.
• Display professional skills in complex multidisciplinary contexts, working in networked teams, whether face-to-face or online, through use of information and communication technology.

Content

0. Statistics and probability in engineering
1. Probability
   1. Introduction to probability
   2. Random variables
   3. Random variable models
2. Statistics
   1. Introduction to statistical inference
   2. Inference to compare populations
   3. Linear models
   4. Quality control

Evaluation

The evaluation of the subject is based in the monitoring of the student's academic work during the course and its active attendance in the classroom. Specifically, the subject grade is calculated as follows:

• Exams (80%)
  • Probability exam (35%), during the course
  • Statistics exam (45%), at the end of the course
• Programming lab and exercises (20%)

There is a recovery exam in which the student can choose one of the two exams to recover: probability or statistics.

The part corresponding to the programming lab and exercises cannot be recovered.

The grade to pass the subject must be gretar or equal than 5. It is not necessary to score a 5 or more in each of the parts to pass.

Methodology

• Master classes (face to face activity)
• Problem-solving sessions (directed activity)
• Programming Labs (directed and autonomous activity)
• Evaluation sessions (face to face activity)
• Autonomous study (autonomous activity)

Bibliography

Key references

• González, José A (2008). Estadística per Enginyers Informàtics. Retrieved from http://hdl.handle.net.biblioremot.uvic.cat/2099.3/36774
• Pozo, F., Parés, N., Vidal, Y., i Mazaira, F. (2010). Probabilitat i estadística matemàtica: Teoria i problemes resolts. Retrieved from http://hdl.handle.net/2099.3/36649

Further reading

Teachers will provide complementary bibliography and compulsory reading throughout the course via the Virtual Campus.