401-0604-00L  Probability Theory and Statistics

SemesterSpring Semester 2020
LecturersV. Tassion
Periodicityyearly recurring course
Language of instructionEnglish (lecture), German (exercise)

AbstractProbability models and applications, introduction to statistical estimation and statistical tests.
ObjectiveAbility to understand the covered methods and models from probability theory and to apply them in other contexts. Ability to perform basic statistical tests and to interpret the results.
ContentThe concept of probability space and some classical models: the axioms of Kolmogorov, easy consequences, discrete models, densities, product spaces, relations between various models, distribution functions, transformations of probability distributions. Conditional probabilities, definition and examples, calculation of absolute probabilities from conditional probabilities, Bayes' formula, conditional distribution. Expectation of a random variable,application to coding, variance, covariance and correlation, linear estimator, law of large numbers, central limit theorem. Introduction to statistics: estimation of parameters and tests
Lecture notesyes
LiteratureTextbuch: P. Brémaud: 'An Introduction to Probabilistic Modeling', Springer, 1988.