# 107.369 Statistics and Probability Theory This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_21",{id:"j_id_21",showEffect:"fade",hideEffect:"fade",target:"isAllSteop"});});This course is in at least 1 assigned curriculum part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_23",{id:"j_id_23",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});}); 2024W 2023W 2022W 2021W 2020W 2019W 2018W 2017W 2016W 2015W 2014W 2013W 2012W 2011W 2010W 2009W 2008W 2007W 2006W

2022W, UE, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: UE Exercise
• Format: Hybrid

## Learning outcomes

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.

## Subject of 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.

## Teaching methods

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.

## Mode of examination

Immanent

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 3, TUE 18.10.2022

Detailed description and plan as well as all announcements and material can be found in TUWEL.

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

## Course dates

DayTimeDateLocationDescription
Tue09:00 - 19:0004.10.2022 - 24.01.2023Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue09:00 - 19:0004.10.2022 - 24.01.2023Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Statistics and Probability Theory - Single appointments
DayDateTimeLocationDescription
Tue04.10.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue04.10.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue11.10.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue11.10.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue18.10.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue18.10.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue25.10.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue25.10.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue08.11.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue08.11.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue22.11.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue22.11.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue29.11.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue29.11.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue06.12.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue06.12.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue13.12.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue13.12.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie
Tue20.12.202209:00 - 19:00Hörsaal 14 UE Statistik und Wahrscheinlichkeitstheorie
Tue20.12.202209:00 - 19:00Seminarraum AE U1 - 5 UE Statistik und Wahrscheinlichkeitstheorie

## Examination modalities

Ongoing performance control

## Group dates

GroupDayTimeDateLocationDescription
Gruppe 1 - 09:00Tue09:00 - 11:0011.10.2022 - 24.01.2023 107.369 Statistics and Probability Theory Gruppe 1 - 09:00
Gruppe 2 - 09:00Tue09:00 - 11:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 2 - 09:00
Gruppe 3 - 11:00Tue11:00 - 13:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 3 - 11:00
Gruppe 4 - 11:00Tue11:00 - 13:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 4 - 11:00
Gruppe 5 - 13:00Tue13:00 - 15:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 5 - 13:00
Gruppe 6 - 13:00Tue13:00 - 15:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 6 - 13:00
Gruppe 7- 15:00Tue15:00 - 17:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 7- 15:00
Gruppe 8 -15:00Tue15:00 - 17:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 8 -15:00
Gruppe 9 - 17:00Tue17:00 - 19:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 9 - 17:00
Gruppe 10 - 17:00Tue17:00 - 19:0011.10.2022 - 24.01.2023 107.369 UE Statistics and Probability Theory - Gruppe 10 - 17:00

## Course registration

Begin End Deregistration end
05.09.2022 07:00 11.10.2022 12:00 06.11.2022 12:00

## Group Registration

GroupRegistration FromTo
Gruppe 1 - 09:0001.09.2022 08:0002.10.2022 12:00
Gruppe 2 - 09:0001.09.2022 07:0009.10.2022 12:00
Gruppe 3 - 11:0001.09.2022 07:0009.10.2022 12:00
Gruppe 4 - 11:0001.09.2022 07:0009.10.2022 12:00
Gruppe 5 - 13:0001.09.2022 07:0009.10.2022 12:00
Gruppe 6 - 13:0001.09.2022 08:0009.10.2022 12:00
Gruppe 7- 15:0005.09.2022 07:0011.10.2022 12:00
Gruppe 8 -15:0001.09.2022 07:0009.10.2022 12:00
Gruppe 9 - 17:0001.09.2022 08:0009.10.2022 12:00
Gruppe 10 - 17:0001.09.2022 08:0009.10.2022 12:00

## Curricula

Study CodeObligationSemesterPrecon.Info
033 526 Business Informatics Mandatory3. Semester
Course requires the completion of the introductory and orientation phase
033 532 Media Informatics and Visual Computing Mandatory3. Semester
Course requires the completion of the introductory and orientation phase
033 533 Medical Informatics Mandatory5. Semester
Course requires the completion of the introductory and orientation phase
033 534 Software & Information Engineering Mandatory3. Semester
Course requires the completion of the introductory and orientation phase
884 Subject: Informatics und Informatics Management Mandatory elective5. Semester
Course requires the completion of the introductory and orientation phase

## Literature

No lecture notes are available.

## Previous knowledge

see above (requirements)

## Miscellaneous

• Attendance Required!

English