Mathematical Statistics, First Course, 4 credits

Matematisk statistik, grundkurs, 4 hp

TAMS79

Main field of study

Mathematics Applied Mathematics

Course level

First cycle

Course type

Programme course

Examiner

Jörg-Uwe Löbus

Director of studies or equivalent

Ingegerd Skoglund

Education components

Preliminary scheduled hours: 40 h
Recommended self-study hours: 67 h
ECV = Elective / Compulsory / Voluntary
Course offered for Semester Period Timetable module Language Campus ECV
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Chinese 3 (Autumn 2017) 2 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - French 3 (Autumn 2017) 2 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - German 3 (Autumn 2017) 2 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Japanese 3 (Autumn 2017) 2 3 Swedish Linköping C
6CIEI Industrial Engineering and Management - International, M Sc in Engineering - Spanish 3 (Autumn 2017) 2 3 Swedish Linköping C
6CIII Industrial Engineering and Management, M Sc in Engineering 3 (Autumn 2017) 2 3 Swedish Linköping C

Main field of study

Mathematics, Applied Mathematics

Course level

First cycle

Advancement level

G1X

Course offered for

  • Industrial Engineering and Management - International, M Sc in Engineering
  • Industrial Engineering and Management, 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

Algebra and calculus, especially differentiation, integration, multiple integration and series.

Intended learning outcomes

The course gives an introduction to the mathematical modelling of random experiments, with a special emphasis on applications in science, technology, and economics. After completing the course the student will be expected to be able to:

  • identify experiments where the result is influenced by random factors.
  • describe the basic concepts and theorems of probability theory, e.g., random variable, density function, and the law of large numbers.
  • construct suitable probabilistic models for random experiments.
  • compute important quantities in probabilistic models, e.g., probabilities and expectations.
  • construct and analyse probabilistic models for certain time-dependent randomly varying quantities, e. g. in form of time discrete Markov chains.
  • follow a basic course in statistics.

Course content

Sample space, events and probabilities. Combinatorics. Conditional probabilities and independent events. Discrete and continuous random variables, their probability distributions, expectations and variances. Normal, exponential, binomial, poisson distributions etc. Functions of random variables. Multidimensional random variables. Law of large numbers and the central limit theorem. Poisson processes. Time discrete Markov chains.

Teaching and working methods

Lectures and tutorials.

Examination

TEN1Written examination4 creditsU, 3, 4, 5

Grades

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

Other information

Supplementary courses:
Mathematical Statistics, second course. Queueing Theory. Probability Theory, second course. Stochastic Processes. Production and Operations Management. Financial Markets and Instruments. 

Department

Matematiska institutionen

Director of Studies or equivalent

Ingegerd Skoglund

Examiner

Jörg-Uwe Löbus

Course website and other links

http://courses.mai.liu.se/GU/TAMS79

Education components

Preliminary scheduled hours: 40 h
Recommended self-study hours: 67 h

Course literature

G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst: Sannolikhetsteori och statistikteori med tillämpningar. Studentlitteratur.
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. <br>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
TEN1

                            
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
TEN1

                            
2.2 Experimentation, investigation, and knowledge discovery
X
X
TEN1

                            
2.3 System thinking

                            
2.4 Attitudes, thought, and learning
X
TEN1

                            
2.5 Ethics, equity, and other responsibilities
X
TEN1

                            
3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION
3.1 Teamwork
X

                            
3.2 Communications
X
TEN1

                            
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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