# 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

2023W, VO, 2.0h, 3.0EC

## Properties

• Semester hours: 2.0
• Credits: 3.0
• Type: VO Lecture
• LectureTube course
• Format: Presence

## Learning outcomes

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

• Use basic counting techniques (multiplication rule, combinations, permutations) to compute probabilities.
• 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 square-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)
• The calculus with probabilities
• Conditional probability and independence, Bayes' theorem
• Random variables, distributions (Bernoulli, binomial, geometric, Poisson, uniform, normal and exponential distributions)
• Quantiles, moments, expectation, variance, covariance, correlation
• Random sample, properties of a random sample, sum of random variables from random sample, sampling from normal distribution, properties of sample mean and sample variance, order statistics
• Law of large numbers, Central limit theorem
• 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 - 11:0002.10.2023 - 22.01.2024Informatikhörsaal - ARCH-INF Lectures
Statistics and Probability Theory - Single appointments
DayDateTimeLocationDescription
Mon02.10.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon09.10.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon16.10.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon23.10.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon30.10.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon06.11.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon13.11.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon20.11.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon27.11.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon04.12.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon11.12.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon18.12.202309:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon08.01.202409:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon15.01.202409:00 - 11:00Informatikhörsaal - ARCH-INF Lectures
Mon22.01.202409:00 - 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.

Important: The exam registration is made in TISS within the registration period.  If you are registered for the exam and are not going to attend it, please deregister in TISS within the deregistration period. Please note that students who do not deregister and do not attend the exam will be blocked for registrations for the following examination term.

Academic integrity: Students in this course are expected to comply with the academic integrity code and to behave with academic honesty.  Academic dishonesty is defined as cheating of any kind, including misrepresenting one's own work, taking credit for the work of others without crediting them and without appropriate authorization, and the fabrication of information.

Plagiarism: All your submitted work should be result of your own thought and research. We take plagiarism seriously; students who are caught plagiarizing will fail the course

## 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
04.09.2023 07:00 10.10.2023 12:00 31.10.2023 18:00

## Curricula

Study CodeObligationSemesterPrecon.Info
033 521 Informatics Mandatory3. Semester
Course requires the completion of the introductory and orientation phase
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 Mandatory3. 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

## Literature

Literature will be discussed in the first lecture.

## Previous knowledge

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

English