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Course info
KMA / PMO
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Course description
Department/Unit / Abbreviation
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KMA
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PMO
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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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Probability Models
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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,
5
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
4
[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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No
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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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No
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Summer semester
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0 / -
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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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Winter + Summer
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Semester taught
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Winter + Summer
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Minimum (B + C) students
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1
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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 |
No
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Fundamental course |
No
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Fundamental theoretical course |
No
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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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To introduce several representatives of random processes and study some of their properties and applications. Poisson process. Markov chains with discrete and continuous time, controlled chains, birth and death processes, queuing theory, MCMC simulation. Random walk, martingales, Wiener process.
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Requirements on student
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FOR SUMMER TERM OF SCHOOL YEAR 2017/2018
To master material treated.
Upon repeated registration of the course, the credit obtained in the previous study of this course is not recognized.
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Content
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FOR WINTER TERM OF SCHOOL YEAR 2017/2018
1. From the theory of probability.
2. Stochastic process.
3. Poisson process.
4. Wiener process.
5. Markov chains with rewards.
6. Controlled chains.
7. Inventory and queuing theory I.
8. Inventory and queuing theory II.
Additional information on the web page http://home.zcu.cz/~friesl/Vyuka/Pmo.html
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Activities
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Fields of study
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Guarantors and lecturers
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Literature
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-
Recommended:
HUŠEK, R., LAUBER, J. Aplikace stochastických procesů I, učební text. Praha : VŠE, 1986.
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Recommended:
Mandl, Petr. Pravděpodobnostní dynamické modely : celost. vysokošk. učebnice pro stud. matematicko-fyz. fakult stud. oboru pravděpodobnost a matem. statistika. Praha : Academia, 1985.
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Recommended:
HUŠEK, R., LAUBER, J. Simulační modely. 1. vyd. Praha : SNTL, 1987.
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Recommended:
Štěpán, Josef. Teorie pravděpodobnosti : Matematické základy : Vysokošk. učebnice pro stud. matematicko-fyz. fakult. Praha : Academia, 1987.
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Recommended:
Prášková, Zuzana; Lachout, Petr. Základy náhodných procesů. Praha : Karolinum, 1998. ISBN 80-7184-688-0.
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On-line library catalogues
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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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Preparation for formative assessments (2-20)
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26
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Presentation preparation (report) (1-10)
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20
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Preparation for an examination (30-60)
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40
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Contact hours
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52
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Total
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138
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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: |
The course assumes knowledge of probability and statistics at least at the introductory course (KMA/PSA) level, more detailed knowledge of probability theory (KMA/TP) would be an advantage. The course also makes use of the apparatus of the other introductory mathematics courses (differential and integral calculus, matrices,...). |
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Learning outcomes
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Knowledge - knowledge resulting from the course: |
To orientate oneself in treated properties of random processes, to be able to derive the results presented, to apply them in practical examples and draw practical conclusions. |
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Assessment methods
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Knowledge - knowledge achieved by taking this course are verified by the following means: |
Oral exam |
Written exam |
Individual presentation at a seminar |
Seminar work |
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Teaching methods
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Knowledge - the following training methods are used to achieve the required knowledge: |
Lecture |
Lecture supplemented with a discussion |
Task-based study method |
Collaborative instruction |
Group discussion |
Self-study of literature |
Interactive lecture |
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