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Course, academic year 2022/2023
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Probability and Statistics 2 - NMAI073
Title: Pravděpodobnost a statistika 2
Guaranteed by: Computer Science Institute of Charles University (32-IUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2022
Semester: winter
E-Credits: 5
Hours per week, examination: winter s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: English, Czech
Teaching methods: full-time
Additional information:
Guarantor: doc. Mgr. Robert Šámal, Ph.D.
Incompatibility : NMAX073
Interchangeability : NMAX073
Is incompatible with: NMAX073
Is interchangeable with: NMAX073
Annotation -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)
More advanced parts of probability and statistics for students of computer science. It will be assumed that the students understand material covered by Probability and Statistics 1.
Course completion requirements -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)

The credit will be given for active participation in tutorials, homeworks and successful completion of tests (the exact weight of each of these criteria is determined by the


The nature of the first two requirements does not make it possible for repeated attempts for the credit.

The teacher can, however, determine alternative conditions for replacing the missing requirements.

The exam will be written or oral. Obtaining the credit is necessary before the final exam.

Literature -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)

G. Grimmett, D. Welsh: Probability - an introduction, Oxford University Press, 2014.

M. Mitzenmacher, E. Upfal: Probability and Computing, Cambridge, 2005.

K. Zvára, J. Štěpán: Pravděpodobnost a matematická statistika, Matfyzpress, Praha 1997.

Syllabus -
Last update: doc. Mgr. Robert Šámal, Ph.D. (03.10.2022)

(The course will be in English if there is somebody signed up who does not understand Czech.)

Markov chains:

basic concept and basic use

probabilistic algorithm for 2-SAT, 3-SAT

stationary distribution and the convergence to it.

Model balls-into-bins: use for analysis of hashing, Poisson approximation, estimates.

Poisson's process

Moment generating functions and the proof of Central Limit Theorem.

Conditional expectation. Coupling.

Bayesian statistics

Fundamentals of Information Theory

Graphical models, belief propagation

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