# 107.254 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"});}); 2023W 2022W 2021W 2020W 2019W 2018W 2017W 2016W 2015W 2014W 2013W 2012W 2011W 2010W 2009W 2008W 2007W 2006W 2005W 2004W 2003W 2002W

2022W, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• 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

This course is an introductory statistics and probability theory course.

• Counting (permutations, combinations)
• Compute probabilities
• Random variables, distributions (Bernoulli, binomial, geometric, Poisson, uniform, normal and exponential distributions), quantiles, mean, variance, covariance, correlation, independence
• Conditional probability, Bayes' theorem
• Law of large numbers, Central limit theorem
• Sampling
• Descriptive Statistics (elementary statistics, frequency table, diagrams, empirical distribution, histograms)
• Significance tests and confidence intervals, analysis of variance, univariate linear regression

## Teaching methods

Lectures and accompanying exercises in the exercise sessions. In the lecture, central concepts will be presented, which will be then practiced and deepened in the exercise sessions on the basis of case studies. Exercises will involve solving problems and the use of R for computation, simulation, and visualization.

## Mode of examination

Written

For students of Informatics.

# Requirements for participation:

1. Successful completion of STEOP.
2. Basic knowledge of linear Algebra and Calculus.

Please note that a detailed course description and plan as well as all announcements and material can be found in TUWEL.

## Course dates

DayTimeDateLocationDescription
Mon09:00 - 11:0003.10.2022 - 23.01.2023Informatikhörsaal - ARCH-INF Lectures
Statistics and Probability Theory - Single appointments
DayDateTimeLocationDescription
Mon03.10.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon10.10.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon17.10.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon24.10.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon07.11.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon14.11.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon21.11.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon28.11.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon05.12.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon12.12.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon19.12.202209:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon09.01.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon16.01.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon23.01.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures

## Examination modalities

Result of the final written exam. The exam is a multiple-choice exam. For each question, there are four possible answers and only one is correct. The one alternative that best completes the statement or answers the question should be chosen by ticking. Ticking more than one answer leads to the question being marked as incorrect. Students are given 90 minutes to solve the exam. You may use a non-programmable calculator and a single, hand-written sheet with the formulas you may need (written on one two-sided A4 format paper). Please note that a copy of a handwritten sheet is not a handwritten sheet and cannot be used in the exam. Computers, smartphones, tablets, notes, books, etc., as well as discussions and consultations with others, are not allowed during the exam. It is mandatory to bring a personal document/ID with picture.

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Wed15:00 - 17:0016.10.2024FH Hörsaal 5 - TPH written02.09.2024 08:00 - 07.10.2024 12:00TISS5. Prüfungstermin W2023

## Course registration

Begin End Deregistration end
05.09.2022 07:00 11.10.2022 12:00 06.11.2022 18:00

## 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

Literature will be discussed in the first lecture.

## Previous knowledge

see above (requirements)

English