The purpose of statistics is to summarize a large amount of data and from this to retrieve useful information.In the course Probability Calculus and Statistics, the theoretical foundations and appropriate statistical methods to reach this goal are discussed. The theoretical part of the course is illustrated by means of a wide range of scientific and technological applications. The practical exercises are given separately. Herethe focus is on the application of statistical methods to a broad range of experimental data.
At the beginning of the course you will get an overview of graphical and numerical representations to summarize data. Then concepts of probability theory are explained and the most important probability distributions introduced. Then we will discuss the methodology to construct confidence intervals and to test statistical hypotheses. Finally, statistical parameter estimation is discussed.
The course-content has the following chapters:
- General introduction : purpose of statistics
- Descriptive statistics : graphical and numerical representation to summarize the data
- Probability theory
- Univariate random variables : discrete and continuous random variables, probability distributions
- Multivariate random variables : joint probability distributions, covariance, correlation and variance
- Estimation of parameters : random sample averages, random sample proportions, random sample variance
- Interval estimation : setting up of reliability intervals
- Hypothesis testing : after a general introduction on testing, we deal with the most important tests for location, dispersion and distribution for different measurement scales and for 1, 2 or more than 2 populations respectively.
- Parameter estimation