Subjects(version: 920)
Probability and Statistics 2 - NMAI073
Title: Pravděpodobnost a statistika 2 Computer Science Institute of Charles University (32-IUUK) Faculty of Mathematics and Physics from 2022 winter 5 winter s.:2/2, C+Ex [HT] unlimited unlimited no taught English, Czech full-time https://iuuk.mff.cuni.cz/~samal/vyuka/2223/PSt2/
Guarantor: doc. Mgr. Robert Šámal, Ph.D. NMAX073 NMAX073 NMAX073 NMAX073
 Annotation - ---CzechEnglish
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 - ---CzechEnglish
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

TA).

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 - ---CzechEnglish
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 - ---CzechEnglish
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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