# 107.254 Statistics and Probability Theory This course is in all assigned curricula part of the STEOP.\$(function(){PrimeFaces.cw("Tooltip","widget_j_id_1y",{id:"j_id_1y",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_20",{id:"j_id_20",showEffect:"fade",hideEffect:"fade",target:"isAnySteop"});});

2019W, VO, 2.0h, 3.0EC

## Properties

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

## 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 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 and interpret descriptive statistics and plots.
• 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.

Particular attention is paid to the use of statistical software (e.g. 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
• 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. You will need to bring your laptop during these sessions and to have installed R Studio on your computer. You will not be expected to use R to do any advance computer programming. The R software can be downloaded from the CRAN website

https://cran.r-project.org

## Mode of examination

Written

For students of Informatics.

## Course dates

DayTimeDateLocationDescription
Thu08:00 - 10:0003.10.2019 - 30.01.2020HS 11 Paul Ludwik Statistics and Probability Theory
Statistics and Probability Theory - Single appointments
DayDateTimeLocationDescription
Thu03.10.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu10.10.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu17.10.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu24.10.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu31.10.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu07.11.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu14.11.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu21.11.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu28.11.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu05.12.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu12.12.201908:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu09.01.202008:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu16.01.202008:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu23.01.202008:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory
Thu30.01.202008:00 - 10:00HS 11 Paul Ludwik Statistics and Probability Theory

## Examination modalities

There will be one final written exam. The exam is a multiple-choice questions exam. For each task, 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. You have to use a pen with either blue or black ink. The processing time is 120 minutes. You may use a non-programmable calculator and a hand- written sheet with the formulas you may need (written on one two-sided A4 format paper). The sheet with formulas should be submitted with the exam. Computers, smartphones, tablets, notes, books, etc., as well as discussions and consultations, are not allowed during the exam. It is mandatory to bring a personal document/ID with picture.

## Exams

DayTimeDateRoomMode of examinationApplication timeApplication modeExam
Wed14:00 - 17:0005.02.2020FH Hörsaal 1 written16.12.2019 12:00 - 31.01.2020 23:59TISS1. Prüfungstermin W2019
Wed14:00 - 17:0005.02.2020Informatikhörsaal written16.12.2019 12:00 - 31.01.2020 23:59TISS1. Prüfungstermin W2019
Wed14:00 - 17:0004.03.2020Informatikhörsaal written24.02.2020 12:00 - 01.03.2020 23:55TISS2. Prüfungstermin W2019
Wed14:00 - 17:0004.03.2020HS 13 Ernst Melan written24.02.2020 12:00 - 01.03.2020 23:55TISS2. Prüfungstermin W2019
Wed15:00 - 18:0010.06.2020Informatikhörsaal written11.05.2020 12:00 - 05.06.2020 23:59TISS3. Prüfungstermin W2019

Not necessary

## Curricula

Study CodeSemesterPrecon.Info
033 526 Business Informatics 3. Semester
Course requires the completion of the introductory and orientation phase
033 532 Media Informatics and Visual Computing 3. Semester
Course requires the completion of the introductory and orientation phase
033 533 Medical Informatics 5. Semester
Course requires the completion of the introductory and orientation phase
033 534 Software & Information Engineering 3. Semester
Course requires the completion of the introductory and orientation phase
884 Subject: Informatics und Informatics Management 5. Semester
Course requires the completion of the introductory and orientation phase

## Literature

Literature will be discussed in the first lecture.

## Previous knowledge

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

German