# Course syllabus D1-PSO - Probability theory and statistical estimations (FCE - 2019/2020 - post-graduate studies)

**Information sheet**ECTS Syllabus

Slovak

**English**

University: | Slovak University of Technology in Bratislava | |||||

Faculty: | Faculty of Civil Engineering | |||||

Course unit code: | D1-PSO | |||||

Course unit title: | Probability theory and statistical estimations | |||||

Mode of delivery, planned learning activities and teaching methods: | ||||||

| ||||||

Credits allocated: | 5 | |||||

Recommended semester/trimester: | Applied Mathematics - doctoral (semi-compulsory), 1. year Applied Mathematics (in english language) - doctoral (semi-compulsory), 1. year | |||||

Level of study: | 3. | |||||

Prerequisites for registration: | none | |||||

Assesment methods: | ||||||

seminar project, final project, exam | ||||||

Learning outcomes of the course unit: | ||||||

Student will get the backgrounds in modern probability theory and mathematical statistics. He/she will understand the relationship between the probability theory and statistics, and he/she will understand the basic notions from the mathematical statistics and its methods. Student will get overview of one- and more-dimensional probability distributions, of estimation methods and of hypothesis testing. Based on this subject, student should be able to analyse and process real statistical data. | ||||||

Course contents: | ||||||

- Basics of probability theory; conditional probability and independence of random events; Bayes theorem and total probability theorem
- Random variable; basic probability distributions, distribution functions, properties of the moments of random variables, limit theorems - Random vectors; joint distribution of random variables, marginal distributions; moments of random vectors; independence of random variables - Random sample and distribution derived for random sampling from the normal distribution - Pointwise and interval estimates of parameters - Fundamentals of statistical hypothesis testing - Application of statistical methods to the samples of real statistical geodetical data | ||||||

Recommended or required reading: | ||||||

| ||||||

Language of instruction: | slovak and english or english | |||||

Notes: | ||||||

Courses evaluation: | ||||||

Assessed students in total: 0 | ||||||

Name of lecturer(s): | doc. RNDr. Jana Kalická, PhD. (examiner, instructor, lecturer, tutor) - slovak, english prof. RNDr. Radko Mesiar, DrSc. (person responsible for course) | |||||

Last modification: | 31. 10. 2017 | |||||

Supervisor: | prof. RNDr. Radko Mesiar, DrSc. and programme supervisor |

*Last modification made by Ing. Peter Korčák on 10/31/2017.*