- The student understands simultaneous distribution functions and densities.
- The student is able to recognize situations where the Poisson distribution arises, and to fruitfully apply it.
- The student can creatively apply various generating functions.
- The student has a theoretical knowledge of concentration phenomena, also in geometric settings.
- The student recognises Markov chains in practical situations, and can apply certain theoretical considerations to them.
|
|
This a continuation of the course "Introduction to Probability", with an eye towards further developments along the lines of Data Science. The concepts of simultaneous distributions will be treated, as will the Poisson distribution and the associated process. The concept of generating functions, a mathematical instrument enabling analytical calculations in often unexpected ways, forms a pivotal role in the course. This in particular is helpful towards developing a theoretical understanding of concentration of measure in probabilistic and geometric settings. The course concludes with the theory of Markov chains and its role in the analysis of large unstructured networks.
|
|
This offering of this course starting from 2021 differs significantly from earlier years, and aims to develop a solid mathematical/theoretical underpinning for Data Science. Though Analyse 2 is not a formal prerequisite, it is recommended (possibly in parallel)
|
|
Introduction to Probability
Analyse 2 recommended before or in parallel.
|
|
Written exam.
There is a potential "bonus" from homework which expires for the retake.
The retake might be offered as an oral examination.
|
|
The course will be given in English.
|
|