FMSF05F

Tillfällig

Probability Theory

7,5

Gemensam kurs, avancerad nivå och forskarnivå

7152 (Matematikcentrum (inst LTH) / Matematisk statistik (LTH))

2020-08-26

Professor Thomas Johansson

Engelska

Varje vårtermin

The course gives a deeper and extended knowledge of probability theory, useful for further studies in, e.g., extreme value theory and stochastic processes with applications.

The course deepens and expands the basic knowledge in probability theory. Central moments in the course are transforms of distribution, conditional expectations, multidimensional normal distribution, and stochastic convergence. Further, the concept of stochastic processes is introduced by a fairly thorough treatment of the properties of the Poisson process.

be able to explain different concepts in stochastic convergence and how they relate to each other,
be able to explain the concepts of characteristic and moment generating functions and how these functions can be used,
be able to describe the multi-dimensional normal distribution and the invariance properties under, e.g., linear combinations and conditioning,
be able to explain the definition and basic properties of the Poisson process.

show the ability to integrate knowledge from the different parts of the course when solving problems.

Föreläsningar

övningar

Skriftlig tentamen

Underkänd, godkänd

Basic course in Mathematical Statistics

Gut, A.: An Intermediate Course in Probability Theory. Springer, 1995.

FMSF05F

2020-08-26

Professor Thomas Johansson