MM835: Probability theory
Comment
Entry requirements
Academic preconditions
Course introduction
with probability models, which is important in regard to the study of
theoretical statistics.
The course builds on the knowledge acquired in
the courses MM548, and gives an academic basis for studying the topics
stochastic processes and mathematical finance, that are part of the
degree.
- Give the competence
to plan and execute scientific projects at a high level, and to manage
work and development situations that are complex, unpredictable and that
require new solving skills. - Give skills to study, analyse, model and solve problems on a high level of abstraction using logical and structured argumentation.
- Give knowledge about advanced models and methods in mathematics
Expected learning outcome
The learning objectives of the courseĀ are that the student demonstrates the ability to:
- reproduce definitions in probability theory within the scope of the course's syllabus
- reproduce results in probability theory, together with their proofs, within the scope of the course's syllabus
- apply the theory to solve problems in probability theory
- relate the results within the scope of the course's syllabus to each other
Content
The following main topics are contained in the course: Random variables, probability measures, distribution functions, expectation, independence, characteristic functions, the normal and multivariate normal distribution, convergence of random variables, central limit theorems, conditional expectation, martingales.
Literature
Examination regulations
Exam element a)
Timing
Tests
Oral examination
EKA
Assessment
Grading
Identification
Language
Examination aids
To be announced during the course
ECTS value
Additional information
Indicative number of lessons
Teaching Method
The course introduces the topics at a general level in lectures and exercises sessions will be devoted to work on exercises based on the topics presented in previous lectures.
Activities during the studyphase. Studying the course material and preparing the weekly exercises, individually or through group work.