Titlebook: Introduction to Statistics; Using Interactive MM Wolfgang Karl Härdle,Sigbert Klinke,Bernd Rönz Textbook 2015 Springer Nature Switzerland A

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Basics,Statistics is the science of collecting, describing, and interpreting data, i.e., the tool box underlying empirical research.

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Probability Theory,Probability theory is concerned with the outcomes of random experiments. These can be either real world processes or thought experiments. In both cases,

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Combinatorics,Combinatorial theory investigates possible patterns of orderings of finitely many elements, composed groups (sets) of such orderings, and the number of these orderings and groups.

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Random Variables,A random variable is a function that assigns (real) numbers to the results of an experiment. Each possible outcome of the experiment (i.e., value of the corresponding random variable) occurs with a certain probability.

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Probability Distributions,In the following section we present some important probability distributions, which are often used in statistics. These distributions can be described using at most three parameters. In general, the greater the number of parameters describing a distribution, the more flexible the distribution will be to model data.

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Laconic

Two-Dimensional Frequency Distribution,In the natural sciences, we can often clearly represent the relationship between two variables by means of a function because it has its origin in physical laws.

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Regression,The main objective of regression analysis is to describe the expectation and dependence of a quantity . on quantities .., .., .. A one-directional dependence is assumed. This dependence can be expressed as a general regression function of the following form:

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Time Series Analysis,A time series is the vector of realizations of a random variable X over the time.