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

• Compute and interpret descriptive statistics and plots. 
• Use basic counting techniques (multiplication rule, combinations, permutations) to compute probability and odds. 
• Compute conditional probabilities directly and using the Bayes theorem, and check for independence of events. 
• Set up and 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 confidence intervals for the mean and variance. 
• Carry out hypothesis testing for the mean and variance. Compute and interpret the p-value for these tests. 
• Compute and interpret the correlation between two variables. 
• Compute and interpret linear regression between two variables. 
• Use statistical software (e.g. 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.
• Descriptive statistics: elementary statistics, numerical summaries, empirical distribution, graphical summaries (histograms, boxplots, scatterplots).
• Inferential statistics: confidence intervals for the mean and variance, hypothesis testing for the mean and variance, the p-value for these tests, nonparametric tests, analysis of variance
• Linear regression (correlation, simple linear model, regression line, coefficient of determination). 

Particular attention is paid to the use of statistical software (e.g. 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. Other software for statistical computing and graphics could be also used. The focus is on methods and tools of descriptive and inferential statistics, core concepts of probability theory and implementation of the statistical analysis methods.

PLEASE NOTE:

The exercise groups start in week 2, TUE 08.10.2019. Please note that there will be an online entrance test in TUWEL that you will be asked to complete at the beginning of the semester (in the period 03.10.2019-04.10.2019.) in order to take this course.

You are required to register for one of the exercise groups listed below. Registration starts on 16.09.2019. and ends on 04.10.2019.  Exercises will only take place at the below listed times (please ignore 'Course Dates' for now). Group 4 will be offered in English.

Groups 1: 12:00

Groups 2 &3 & 5: 14:00

Group 4: in English, 14:00

Group 6: 15:00

Groups 7 & 8: 16:00

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

Ongoing performance control

The course attendance is only possible after the completion of the STEOP and the completing the entrance test. The understanding of Linear Algebra and Calculus is required.