Syllabus academic year 2011/2012
(Created 2011-09-01.)
 PROBABILITY THEORY FMSF05
Credits: 7,5. Grading scale: TH. Cycle: G2 (First Cycle). Main field: Technology. Language of instruction: The course might be given in English. FMSF05 overlaps following cours/es: MASC01. Optional for: F4, F4fm, I4, I4fir, Pi4, Pi4fm. Course coordinator: Director of studies Anna Lindgren, studierektor@matstat.lu.se, Mathematical Statistics. Prerequisites: FMS012/FMS032/FMS035/FMS086/FMS140 Mathematical statistics. Assessment: Written and oral exam. Further information: The course is also given at the Faculty of Science with the code MASC01. Home page: http://www.maths.lth.se/matstat/kurser/fmsf05/.

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

Knowledge and understanding
For a passing grade the student must

• 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 descibe 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.

Skills and abilities
For a passing grade the student must

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

Contents
The course deapens 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 thourough treatment of the properties of the Poisson process.

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