Probability, first course, 4 credits

Sannolikhetslära, 4 hp

TAMS14

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Torkel Erhardsson

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 38 h
Recommended self-study hours: 69 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 6 (Spring 2017) 2 4 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 6 (Spring 2017) 2 4 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 6 (Spring 2017) 2 4 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 6 (Spring 2017) 2 4 Swedish Linköping C
6CYYI Applied Physics and Electrical Engineering - International, M Sc in Engineering 6 (Spring 2017) 2 4 Swedish Linköping C
6CYYY Applied Physics and Electrical Engineering, M Sc in Engineering 4 (Spring 2017) 2 4 Swedish Linköping C
6CMED Biomedical Engineering, M Sc in Engineering 4 (Spring 2017) 2 4 Swedish Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Biomedical Engineering, M Sc in Engineering
  • Applied Physics and Electrical Engineering, M Sc in Engineering
  • Applied Physics and Electrical Engineering - International, M Sc in Engineering

Entry requirements

Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshold requirements for progression within the programme, or corresponding.

Prerequisites

Linear algebra, differential and integral calculus, series.

Intended learning outcomes

The aim of the course is to provide an introduction to the mathematical modelling of random experiments. The emphasis is on methods applicable to problems in engineering, economy and natural sciences. After completing the course the student should have the knowledge and skills required to:

  • identify experimental situations where random factors may affect the results.
  • construct relevant probabilistic models for simple random experiments.
  • describe the basic concepts and theorems of probability theory, such as random variable, distribution function and the law of total probability.
  • compute important quantities in probabilistic models, e.g., probabilities and expectations.
  • follow a basic course in statistical theory.

Course content

Sample space, events and probabilities. Combinatorics. Conditional probabilities and independent events. Discrete and continuous random variables. Distribution functions, probability mass functions, probability density functions. Conditional distributions and independent random variables. Functions of random variables. Expectation, variance, standard deviation, covariance, correlation coefficient. Particular distributions, e.g., Gaussian, exponential, uniform, binomial and Poisson distributions. Law of large numbers and the central limit theorem. The Poisson process.

Teaching and working methods

Lectures and tutorials, dealing with theory and exercises.

Examination

TEN1Written examination4 creditsU, 3, 4, 5

Grades

Four-grade scale, LiU, U, 3, 4, 5

Other information

Supplementary courses: Statistics, basic course. Stochastic Processes. Probability Theory, Second course. Probability and Bayesian Networks. Queueing Theory. Digital Image Processing. Signal Theory.

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Torkel Erhardsson

Course website and other links

http://courses.mai.liu.se/GU/TAMS14

Education components

Preliminary scheduled hours: 38 h
Recommended self-study hours: 69 h

Course literature

G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst: Sannolikhetsteori och statistikteori med tillämpningar. Studentlitteratur. Exempelsamling utgiven av institutionen. Institutionens formelsamling i matematisk statistik.
Code Name Scope Grading scale
TEN1 Written examination 4 credits U, 3, 4, 5

Regulations (apply to LiU in its entirety)

The university is a government agency whose operations are regulated by legislation and ordinances, which include the Higher Education Act and the Higher Education Ordinance. In addition to legislation and ordinances, operations are subject to several policy documents. The Linköping University rule book collects currently valid decisions of a regulatory nature taken by the university board, the vice-chancellor and faculty/department boards.

LiU’s rule book for education at first-cycle and second-cycle levels is available at http://styrdokument.liu.se/Regelsamling/Innehall/Utbildning_pa_grund-_och_avancerad_niva. 

G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst: Sannolikhetsteori och statistikteori med tillämpningar. Studentlitteratur. Exempelsamling utgiven av institutionen. Institutionens formelsamling i matematisk statistik.

Note: The course matrix might contain more information in Swedish.

I = Introduce, U = Teach, A = Utilize
I U A Modules Comment
1. DISCIPLINARY KNOWLEDGE AND REASONING
1.1 Knowledge of underlying mathematics and science (G1X level)
X
X
X

                            
1.2 Fundamental engineering knowledge (G1X level)

                            
1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level)

                            
1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level)

                            
1.5 Insight into current research and development work

                            
2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES
2.1 Analytical reasoning and problem solving
X
X
X

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X

                            
2.5 Ethics, equity, and other responsibilities
X

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork

                            
3.2 Communications

                            
3.3 Communication in foreign languages

                            
4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT
4.1 External, societal, and environmental context

                            
4.2 Enterprise and business context

                            
4.3 Conceiving, system engineering and management

                            
4.4 Designing

                            
4.5 Implementing

                            
4.6 Operating

                            
5. PLANNING, EXECUTION AND PRESENTATION OF RESEARCH DEVELOPMENT PROJECTS WITH RESPECT TO SCIENTIFIC AND SOCIETAL NEEDS AND REQUIREMENTS
5.1 Societal conditions, including economic, social, and ecological aspects of sustainable development for knowledge development

                            
5.2 Economic conditions for knowledge development

                            
5.3 Identification of needs, structuring and planning of research or development projects

                            
5.4 Execution of research or development projects

                            
5.5 Presentation and evaluation of research or development projects

                            

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