Probability models and applications, introduction to statistical estimation and statistical tests.
Learning objective
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.
Content
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, law of large numbers, central limit theorem. Introduction to statistics: estimation of parameters and tests
Lecture notes
yes
Literature
Textbuch: P. Brémaud: 'An Introduction to Probabilistic Modeling', Springer, 1988.
Performance assessment
Performance assessment information (valid until the course unit is held again)
Performance assessment as a semester course
In examination block for
Bachelor's Degree Programme in Computational Science and Engineering 2018; Version 13.12.2022 (Examination Block G3) Bachelor's Degree Programme in Electrical Engineering and Information Technology 2016; Version 31.10.2017 (Examination Block 3) Bachelor's Degree Programme in Electrical Engineering and Information Technology 2017; Version 07.04.2022 (Examination Block 3)
The performance assessment is offered every session. Repetition possible without re-enrolling for the course unit.
Mode of examination
written 90 minutes
Additional information on mode of examination
Als (freiwillige) Lernelemente werden zwei Quizzes (gegen Ende März und Mitte Mai) angeboten, welche einen Bonus von maximal 0.25 Notenpunkten zur Endnote beitragen können.
Written aids
5 beidseitig von Hand beschriebene A4-Blätter, keine Taschenrechner.
If the course unit is part of an examination block, the credits are allocated for the successful completion of the whole block. This information can be updated until the beginning of the semester; information on the examination timetable is binding.
Performance assessment as a semester course