# Stochastics

What is Stochastics:

Stochastics is a branch of mathematics. The term stochastics summarizes the fields of probability theory and statistics as an umbrella term:

• Probability theory is a branch of mathematics that deals with the modeling and study of random events.
• Statistics is the study of methods for dealing with quantitative information (data). It provides a systematic link between experience (empiricism) and theory.

(according to Wikipedia: stochastics, probability theory, statistics).

Aim of the lecture:

The aim of the lecture is the independent development of solution concepts using methods of stochastics. This requires the development of mathematical creativity. Often students are familiar with the necessary mathematical tools, but not with the step from the problem to the model to which these tools can be applied.

Contents of the lecture

The following topics will be covered in the lecture:

• Descriptive statistics
• Probability
• Simulation and random numbers
• Random variable, expected value and variance
• Special discrete distributions
• Inequality of Chebyshev, Weak law of large numbers
• General probability spaces
• Probability measures on (R, B(I))
• Estimating
• Testing
• Further questions

Literature:

The literature used is:H. Kütting, M. J. SauerElementare Stochastik - Mathematische Grundlagen und didaktische KonzepteSpektrum Akademischer Verlag, Heidelberg 3rd edition, 2011This book is available as an e-book from the University Library Kassel:https://link.springer.com/book/10.1007/978-3-8274-2760-1

Exercise Content:

The exercises cover the topics addressed in the lecture. In addition, exercise sheets are discussed in the exercise, which are to be worked out independently in advance. Some of the exercises have to be handed in. The quality of the assignments will determine whether the student passes the course work, which is a prerequisite for admission to the examination.