| TAMS15 |
Mathematical Statistics, First Course, 6 ECTS credits.
/Matematisk statistik I, grundkurs/
For:
Mat
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Prel. scheduled
hours: 52
Rec. self-study hours: 108
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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 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.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Algebra and calculus, especially differentiation, integration, multiple integration and 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:
Mathematical Statistics, second course. Queueing Theory. Probability Theory, second course. Stochastic Processes. Production and Operations Management. Financial Markets and Instruments.
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Organisation:
Lectures and tutorials.
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Course contents:
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.
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Course literature:
G. Blom, J. Enger, G. Englund, J. Grandell, L. Holst: Sannolikhetsteori och statistikteori med tillämpningar, Studentlitteratur.
Handbook of formulas published by the department.
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Examination: |
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Written examination
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6 ECTS
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Course language is Swedish.
Department offering the course: MAI.
Director of Studies: Ingegerd Skoglund
Examiner: Jörg-Uwe Löbus
Link to the course homepage at the department
Course Syllabus in Swedish
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