Probability theory provides the formal mathematical language to describe and analyze processes with an uncertain outcome. The number of claims (and the amount of damage) an insurance company has to handle, the gain of an asset within a quarter, the spread of a virus or the concentration of a pollutant are just a few real life examples of processes which – due to their complexity – cannot be described by some deterministic physical model. This is why we then use a “stochastic” approach: we a assign a probability, i.e. a measures of uncertainty, to the event of interest.
The objective of this course is to review some main concepts of modern probability theory. The student will be familiarized with probabilistic language and concepts. At the end of the course the students will have acquainted a solid knowledge which allows them to follow other courses in the master program which are founded on probabilistic formalism.