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Main menu for Browse IS/STAG
Course info
KKY / STP
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Course description
Department/Unit / Abbreviation
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KKY
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STP
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Academic Year
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2023/2024
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Academic Year
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2023/2024
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Title
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Stochastic Systems and Processes
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Form of course completion
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Exam
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Form of course completion
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Exam
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Accredited / Credits
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Yes,
6
Cred.
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Type of completion
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Combined
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Type of completion
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Combined
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Time requirements
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Lecture
3
[Hours/Week]
Tutorial
2
[Hours/Week]
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Course credit prior to examination
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Yes
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Course credit prior to examination
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Yes
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Automatic acceptance of credit before examination
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Yes in the case of a previous evaluation 4 nebo nic.
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Included in study average
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YES
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Language of instruction
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Czech
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Occ/max
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Automatic acceptance of credit before examination
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Yes in the case of a previous evaluation 4 nebo nic.
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Summer semester
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30 / -
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0 / -
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0 / -
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Included in study average
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YES
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Winter semester
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0 / -
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0 / -
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0 / -
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Repeated registration
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NO
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Repeated registration
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NO
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Timetable
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Yes
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Semester taught
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Summer semester
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Semester taught
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Summer semester
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Minimum (B + C) students
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10
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Optional course |
Yes
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Optional course
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Yes
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Language of instruction
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Czech
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Internship duration
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0
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No. of hours of on-premise lessons |
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Evaluation scale |
1|2|3|4 |
Periodicity |
každý rok
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Evaluation scale for credit before examination |
S|N |
Periodicita upřesnění |
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Fundamental theoretical course |
Yes
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Fundamental course |
No
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Fundamental theoretical course |
Yes
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Evaluation scale |
1|2|3|4 |
Evaluation scale for credit before examination |
S|N |
Substituted course
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None
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Preclusive courses
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N/A
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Prerequisite courses
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N/A
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Informally recommended courses
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N/A
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Courses depending on this Course
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N/A
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Histogram of students' grades over the years:
Graphic PNG
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XLS
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Course objectives:
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The aim of the course is to introduce students to basic properties of stochastic systems and processes.
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Requirements on student
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Test and elaboration of two written reports and to understand content of the lectures.
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Content
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1.Introduction, description of reality and uncertainty, deterministic and stochastic approach, relation, projection,topological space,
2.Measurable space and projection, Lebesque and Radon-Nikodin theorems,
3.Probability and decision making in control, probability space,
4.Conditional probability,independence,Bayesian theorem, random variables and their description,
5.Vector random variable,distribution function, probability density functions, moments,
6.Transformation of random variables,
7.Random processes and their description,
8.Markov, Gaussian, white, Poisson, stacionary, ergodic processes,
9.Introduction to stochastic system theory, causal stochastic system,
10.Phenomenological and state theory for stochastic systems,
11.Linear stochastic system, state space and input outpu models,
12.Linear stochastic system, description of input, state and output processes,
13.Spectral factorization of discrete time random process.
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Activities
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Fields of study
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Guarantors and lecturers
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Guarantors:
Doc. Ing. Ondřej Straka, Ph.D. (100%),
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Lecturer:
Doc. Ing. Ondřej Straka, Ph.D. (100%),
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Tutorial lecturer:
Ing. Jiří Ajgl, Ph.D. (100%),
Ing. Oliver Kost, Ph.D. (100%),
Doc. Ing. Ondřej Straka, Ph.D. (100%),
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Literature
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Time requirements
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All forms of study
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Activities
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Time requirements for activity [h]
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Contact hours
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39
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Practical training (number of hours)
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26
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Undergraduate study programme term essay (20-40)
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30
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Preparation for formative assessments (2-20)
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20
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Preparation for an examination (30-60)
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50
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Total
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165
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Prerequisites
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Knowledge - students are expected to possess the following knowledge before the course commences to finish it successfully: |
disponovat znalostmi základních technik integrálního počtu |
disponovat znalostmi základů lineární algebry |
disponovat znalostmi základů teorie pravděpodobnosti |
Skills - students are expected to possess the following skills before the course commences to finish it successfully: |
kombinovat pravděpodobnosti nad množinami jevů |
použít techniky integrálního počtu při práci s náhodnými veličinami |
pracovat s maticemi, analyzovat jejich vlastnosti |
Competences - students are expected to possess the following competences before the course commences to finish it successfully: |
N/A |
N/A |
N/A |
N/A |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
charakterizovat náhodné veličiny |
charakterizovat neurčitosti přítomné v systému |
charakterizovat stochastický proces |
vyjádřit rozdíl mezi deterministickým a stochastickým systémem |
Skills - skills resulting from the course: |
analyzovat vlastnosti náhodných procesů přítomných v systému |
konstruovat lineární model popisující stochastický systém spojitý i diskrétní v čase |
popsat stochastický systém včetně charakteristik neurčitostí |
vyjádřit pravděpodobnostní závislosti mezi procesy přítomnými v systému |
využít Bayesův přístup při zpracování informace |
Competences - competences resulting from the course: |
N/A |
N/A |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Combined exam |
Test |
Skills - skills achieved by taking this course are verified by the following means: |
Seminar work |
Competences - competence achieved by taking this course are verified by the following means: |
Combined exam |
Seminar work |
Test |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Skills - the following training methods are used to achieve the required skills: |
Individual study |
Practicum |
Competences - the following training methods are used to achieve the required competences: |
Individual study |
Lecture |
Practicum |
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