| TAMS46 |
Probability Theory, Second Course, 6 ECTS credits.
/Sannolikhetslära, fortsättningskurs/
For:
I
Ii
Mat
MMAT
Y
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Prel. scheduled
hours: 48
Rec. self-study hours: 112
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Area of Education: Science
Main field of studies: Mathematics, Applied Mathematics
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Advancement level
(G1, G2, A): A
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Aim:
The course gives knowledge of
probability theory at an advanced undergraduate level. After
completing the course the student will be expected to be able to:
- describe advanced concepts and theorems of probability theory, e.g., different kinds of stochastic convergence and the Cramer-Slutsky theorem, and to prove some of the theorems.
- construct and analyse probabilistic models using advanced tools and methods, e.g., characteristic functions and conditioning.
- describe and prove some basic theorems of statistics.
- understand and assess probabilistic models and analyses occurring in other undergraduate courses, research reports, or the media.
- follow a graduate course in probability theory, and an advanced undergraduate course in statistics.
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Prerequisites: (valid for students admitted to programmes within which the course is offered)
Linear algebra and multivariate analysis. Basic courses in probability and statistics.
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:
Statistical Theory, Advanced Course. Stochastic processes applied to finance.
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Organisation:
Teaching is performed in groups and consists of lessons dealing with theory and exercises.
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Course contents:
The transformation theorem. Conditioning. Probability generating function, moment generating function, characteristic function. Order statistics. The multivariate normal distribution, in particular orthogonal transformations and quadratic forms. Convergence concepts, e.g., convergence almost surely, in probability, in r-mean, and in distribution. The Borel-Cantelli lemma and the continuity theorem. The law of large numbers and the central limit theorem. The Cramer-Slutsky theorem.
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Course literature:
Gut, Allan: An Intermediate Course in Probability, 2nd ed. Springer (2009).
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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: Torkel Erhardsson
Link to the course homepage at the department
Course Syllabus in Swedish
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