| TAMS36 |
Probability, First Course, 4 ECTS credits.
/Sannolikhetslära/
For:
IT
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Prel. scheduled
hours: 52
Rec. self-study hours: 55
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): G1
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Aim:
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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Calculus, algebra, differential and integral calculus, power series.
Note: Admission requirements for non-programme students usually also include admission requirements for the programme and threshhold requirements for progression within the programme, or corresponding.
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Supplementary courses:
Statistics, Digital Image Processing, Signal Theory
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Organisation:
Teaching consists of lectures and lessons dealing with theory and exercises together with work in PBL-group.
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Course contents:
- 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.
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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.
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Examination: |
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Written examination
Tutorial work
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3 ECTS
1 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Torkel Erhardsson
Link to the course homepage at the department
Course Syllabus in Swedish
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