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Probability, First Course, 4 credits
Sannolikhetslära, 4 hp
TAMS36
Main field of study
Mathematics Applied MathematicsCourse level
First cycleCourse type
Programme courseExaminer
Torkel ErhardssonDirector of studies or equivalent
Ingegerd SkoglundEducation components
Preliminary scheduled hours: 52 hRecommended self-study hours: 55 h
ECV = Elective / Compulsory / Voluntary
| Course offered for | Semester | Period | Timetable module | Language | Campus | ECV | |
|---|---|---|---|---|---|---|---|
| 6CITE | Information Technology, M Sc in Engineering | 4 (Spring 2017) | 2 | 4 | Swedish | Linköping, Valla | C |
Main field of study
Mathematics, Applied MathematicsCourse level
First cycleAdvancement level
G1XCourse offered for
- Information Technology, 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
Calculus, algebra, differential and integral calculus, power 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 influence may affect the results.
- construct relevant probabilistic models for simple random experiments.
- describe basic concepts and theorems of probability theory, e.g., random variable, distribution function and the law of total probability.
- compute important quantities in probabilistic models, e.g., probabilities and expectations.
Course content
- Definition of probability
- Combinatorial methods
- Conditional probability and Bayes rule
- Discrete random variables, probability function, cumulative distribution function.
- Expected value, variance, covariance, correlation
- Special examples: Bernoulli, Binomial, Geometric, Hypergeometric, Negative Binomial, Poisson, and applications.
- Joint probability functions, conditional probability function, conditional expectation.
- Continuous random variables
- Special distributions: the exponential distribution, the normal distribution.
- Sampling and the Central Limit Theorem.
- The Poisson Process and applications.
- Scenarios illustrating applications of probability and statistics.
Teaching and working methods
Teaching consists of lectures and lessons dealing with theory and exercises together with work in PBL-group.
Examination
| BAS1 | Tutorial work | 1 credits | U, G |
| TEN1 | Written examination | 3 credits | U, 3, 4, 5 |
Grades
Four-grade scale, LiU, U, 3, 4, 5Other information
| Supplementary courses: Statistics, Digital Image Processing, Signal Theory |
Department
Matematiska institutionenDirector of Studies or equivalent
Ingegerd SkoglundExaminer
Torkel ErhardssonCourse website and other links
http://courses.mai.liu.se/GU/TAMS36Education components
Preliminary scheduled hours: 52 hRecommended self-study hours: 55 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 |
|---|---|---|---|
| BAS1 | Tutorial work | 1 credits | U, G |
| TEN1 | Written examination | 3 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.
Course literature is preliminary.
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
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X
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X
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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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| 2.2 Experimentation, investigation, and knowledge discovery |
X
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X
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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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| 2.5 Ethics, equity, and other responsibilities |
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X
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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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| 3.3 Communication in foreign languages |
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X
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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 |
X
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X
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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 |
X
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X
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