The course covers random variables in one and several dimensions, conditional probabilities, probability generating and characteristic functions. The multivariate normal distribution and distributions of order statistics and quadratic forms are treated. Other important probabilistic results that are covered more thoroughly compared to courses on the Bachelor level, are covergence criteria for series of random variables, the Borel Cantelli lemma, convergence through transforms, the law of large numbers, the central limit theorem and Cramér-Slutsky's theorem. Finally a deepend presentation of Poisson processes is given.
The course requires 90 ECTS including courses in Mathematical Statistics minimum 12 ECTS or courses in Statistics, minimum 75 ECTS and in both cases a course in Basic Calculus, 7,5 ECTS. Proficiency in English and Swedish equivalent to the level required for basic eligibility for higher studies.