Probability models and applications, introduction to statistical estimation and statistical tests.
Ability 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.
The 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, conditional expectation, law of large numbers, central limit theorem. Introduction to statistics: estimation of parameters and tests
Textbuch: P. Brémaud: 'An Introduction to Probabilistic Modeling', Springer, 1988.