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Mathematical Statistics, first course, 6 credits
Matematisk statistik I, grundkurs, 6 hp
TAMS15
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Jörg-Uwe LöbusDirector of studies or equivalent
Ingegerd SkoglundEducation components
Preliminary scheduled hours: 52 hRecommended self-study hours: 108 h
ECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6KMAT | Mathematics, Bachelor´s Programme | 3 (Autumn 2017) | 2 | 3 | Swedish | Linköping, Valla | C |
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G1XCourse offered for
- Mathematics, Bachelor´s Programme
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 continuous 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, covariance and correlation. Law of large numbers and the central limit theorem. Poissonprocesses. Birth- and death-processes. Brownian motion.
Teaching and working methods
Lectures and tutorials.
Examination
| TEN1 | Examination | 6 credits | U, 3, 4, 5 |
Grades
Alternative-grade scale, LiU, U, 3, 4, 5Other 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 institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Jörg-Uwe LöbusCourse website and other links
http://courses.mai.liu.se/GU/TAMS15Education components
Preliminary scheduled hours: 52 hRecommended self-study hours: 108 h
Course literature
Additional literature
Books
- G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst, Sannolikhetsteori och statistikteori med tillämpningar Studentlitteratur
Compendia
- Institutionens formelsamling i matematisk statistik
| Code | Name | Scope | Grading scale |
|---|---|---|---|
| TEN1 | Examination | 6 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.
Additional literature
Books
G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst, Sannolikhetsteori och statistikteori med tillämpningar Studentlitteratur
Compendia
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
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X
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X
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TEN1
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| 1.2 Fundamental engineering knowledge (G1X level) |
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| 1.3 Further knowledge, methods, and tools in one or several subjects in engineering or natural science (G2X level) |
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| 1.4 Advanced knowledge, methods, and tools in one or several subjects in engineering or natural sciences (A1X level) |
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| 1.5 Insight into current research and development work |
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| 2. PERSONAL AND PROFESSIONAL SKILLS AND ATTRIBUTES | ||||||
| 2.1 Analytical reasoning and problem solving |
X
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X
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X
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TEN1
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| 2.2 Experimentation, investigation, and knowledge discovery |
X
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X
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TEN1
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| 2.3 System thinking |
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| 2.4 Attitudes, thought, and learning |
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X
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TEN1
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| 2.5 Ethics, equity, and other responsibilities |
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X
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TEN1
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| 3. INTERPERSONAL SKILLS: TEAMWORK AND COMMUNICATION | ||||||
| 3.1 Teamwork |
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X
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| 3.2 Communications |
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X
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TEN1
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| 3.3 Communication in foreign languages |
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| 4. CONCEIVING, DESIGNING, IMPLEMENTING AND OPERATING SYSTEMS IN THE ENTERPRISE, SOCIETAL AND ENVIRONMENTAL CONTEXT | ||||||
| 4.1 External, societal, and environmental context |
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| 4.2 Enterprise and business context |
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| 4.3 Conceiving, system engineering and management |
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| 4.4 Designing |
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| 4.5 Implementing |
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| 4.6 Operating |
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| 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 |
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| 5.2 Economic conditions for knowledge development |
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| 5.3 Identification of needs, structuring and planning of research or development projects |
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| 5.4 Execution of research or development projects |
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| 5.5 Presentation and evaluation of research or development projects |
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