After successful completion of the course, students are able to: 

• Use basic counting techniques (multiplication rule, combinations, permutations) to compute probability. 
• Compute conditional probabilities directly and using Bayes theorem, and check for independence of events.
• Work with discrete random variables. In particular, understand the Bernoulli, binomial, geometric and Poisson distributions.
• Work with continuous random variables. In particular, know the properties of uniform, normal and exponential distributions.
• Know what expectation and variance mean and compute them.
• Understand the law of large numbers and the central limit theorem.
• Compute and interpret descriptive statistics and plots.
• Compute confidence intervals for estimators.
• Carry out  and interpret hypothesis tests (t-tests, ANOVA, chi^2-test, frequncies) as well as compute and interpret the p-value.
• Compute and interpret the correlation between two variables.
• Compute and interpret univariate linear regression models.
• Use the statistical software R to implement the statistical analysis methods covered in the course.

• Probability theory: discrete and continuous random variables, expectation and variance, independence, correlation between two random variables, central limit theorem, law of large numbers
• Descriptive statistics: elementary statistics, numerical summaries, empirical distribution, graphical summaries (histograms, boxplots, scatterplots).
• Inferential statistics: confidence intervals, hypothesis testing (t-tests, ANOVA, chi^2-tests, proportions), the p-value for these tests
• Linear regression (correlation, simple linear model, regression line). 

Particular attention is paid to the use of statistical software R to implement the statistical analysis. For more details please see LV 107.254.

Main concepts of the course will be presented in the lectures LV Nr. 107.254 and then will be practiced and deepened in the Exercise sessions LV Nr. 107.369. Exercise sessions will involve solving problems and the use of R for computation, simulation, and visualization. The focus is on methods of descriptive and inferential statistics, core concepts of probability theory, and implementation of the statistical analysis methods.

For students of Informatics. 

Requirements for participation:

1. Registration in the course via the corresponding TISS page within the registration period.
2. Successful completion of STEOP.
3. Basic knowledge of linear Algebra and Calculus.

Please note, the exercise groups start in week 2, THU 14.10.2021.

Please note that the exercises will be held online. Detailed description and plan can be found in TUWEL.

The lecture & exercises (Statistics and Probability Theory) are offered both in the summer and winter semester.

Ongoing performance control

see above (requirements)