![[DPrav] Discrete Probability](https://www.kis.fri.uniza.sk/wp-content/themes/Divi-child/imgs/KIS-subject-default.png)
Main objectives of the course:
Basic knowledge of the theory of probability, random trials, random events and processes and solving of the basic problems in probability.
| Course information sheet | |||||||||||||
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| University: University of Žilina | |||||||||||||
| Faculty: Faculty of Management Science and Informatics | |||||||||||||
| Course ID: 5BA124 | Course name: Discrete Probability (DPrav) | ||||||||||||
| Form, extent and method of teaching activities: | |||||||||||||
| Number of classes per week in the form of lectures, laboratory exercises, seminars or clinical practice | Lectures: 2.0 Seminars: 2.0 Lab.exercises: 1.0 | ||||||||||||
| Methods by which the educational activity is delivered | Present form of education | ||||||||||||
| Applied educational activities and methods suitable for achieving learning outcomes | |||||||||||||
| Number of credits: 6.0 | |||||||||||||
| Study workload: hours Specification of the study workload: | |||||||||||||
| Recommended term of study: 1. year, summer semester | |||||||||||||
| Study degree: 1. | |||||||||||||
| Required subsidiary courses: Prerequisites: 5BF115 Mathematics for Informatics Co-requisites: | |||||||||||||
| Course requirements: Continuous assessment / evaluation: Continuous assessment: Working at term: 72% Semester work written: Exam: 28% The examination is a test of the theory and examples. For the test, it is possible to obtain 20 points of which must be at least 12 to continue the experimental section. For computer problems you can get 8 points of which must be received at least 4. For problems you can get 12 points of which must be received at least 6. Finally, add up the points gained through semester and during the test. Final assessment /evaluation: Final score: Rating points obtained by: 91-100 points A; 81-90 points B; 71-80 points C; 61-70 points D; 53-60 points E; less than 53 points FX. To enroll for an exam student must have 42 points. | |||||||||||||
| Course outcomes: Basic knowledge of the theory of probability, random trials, random events and processes and solving of the basic problems in probability. | |||||||||||||
| Course scheme: Lectures: 1-2. Binomial coefficients: counting of subsets, sequences of subsets, binomial theorem, combinatorial proof. 3-4. Generating functions: Generating function, operations on generating functions, Fibonacci sequence, counting with generating functions. 5-6. Discrete probability: the four step method, infinite sample spaces, conditional probability, independence, mutual independence. 7. Counting of probability: total probability formula, Bayes theorem. 8. Random variables, distribution, sampling: random variable and events, pigeon holes problem, distribution, random sample a confidence interval. 9-10. Expectation and variance: Mean, Markov’s theorem, Chebyshev’s theorem, variance, standard deviation, estimation by random sampling, pair wise independent sampling, probabilistic generating function, hashing. 11. Discrete stochastic process: State of the process, graph of transmissions, throwing the coin, random walk, ergodic Markov chain, matrix of the transmissions probabilities, invariant and asymptotic distribution of states. 12. Elementary models of production rate: request’s flow and service, system Geo/Geo/1, stochastic research. Seminars and Laboratory work: 1-2. Binomial coefficients, 3-4. Generating functions, 5-6. Discrete probability, 7. Counting of probability, 8. Random variables, distribution, sampling, 9-10. Expectation and variance, 11. Discrete stochastic process, 12. Elementary models of production rate | |||||||||||||
| Literature: Meyer, A.R.: Mathematics for Computer Science, MIT 2007, pp. 403-560 Hynek Bachratý, Marián Grendár, Katarína Bachratá: Ako sa počíta pravdepodobnosť? EDIS 2010 Graham, R., Knuth, D., Pataschnik, O. - Concrete mathematics, Addison-Wesley, 1990, ISBN 0-201-14236-8 https://stellar.mit.edu/S/course/6/fa13/6.042/ | |||||||||||||
| Instruction language: slovak | |||||||||||||
| Notes: | |||||||||||||
| Course evaluation:: Total number of evaluated students: 1383
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| A | B | C | D | E | FX | ||||||||
| 8.32 % | 15.33 % | 26.03 % | 28.42 % | 6.65 % | 15.26 % | ||||||||
| Course teachers: Lecture: doc. RNDr. Katarína Bachratá, PhD. Lecture: RNDr. Hynek Bachratý, PhD. Laboratory: doc. RNDr. Katarína Bachratá, PhD. Laboratory: RNDr. Hynek Bachratý, PhD. Laboratory: Mgr. Alžbeta Bohiniková, PhD. Laboratory: Mgr. Katarína Buzáková Laboratory: Mgr. Kristína Ďuračíková, PhD. Laboratory: Ing. René Fabricius Laboratory: Mgr. Iveta Jančigová, PhD. Laboratory: Mgr. Peter Novotný, PhD. Laboratory: doc. Mgr. Juraj Smieško, PhD. Laboratory: Mgr. Monika Smiešková, PhD. Seminar: doc. RNDr. Katarína Bachratá, PhD. Seminar: RNDr. Hynek Bachratý, PhD. Seminar: Mgr. Alžbeta Bohiniková, PhD. Seminar: Mgr. Katarína Buzáková Seminar: Mgr. Kristína Ďuračíková, PhD. Seminar: Ing. René Fabricius Seminar: Mgr. Iveta Jančigová, PhD. Seminar: Mgr. Peter Novotný, PhD. Seminar: doc. Mgr. Juraj Smieško, PhD. Seminar: Mgr. Monika Smiešková, PhD. | |||||||||||||
| Last updated: 2021-12-10 13:59:13.000 | |||||||||||||
| The person responsible for the course: doc. RNDr. Katarína Bachratá, PhD. | |||||||||||||
| Approved by: prof. Ing. Pavel Segeč, PhD. | |||||||||||||