SubjectsSubjects(version: 899)
Course, academic year 2021/2022
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Probability and Statistics 1 - NMAI059
Title: Pravděpodobnost a statistika 1
Guaranteed by: Computer Science Institute of Charles University (32-IUUK)
Faculty: Faculty of Mathematics and Physics
Actual: from 2021
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2 C+Ex [hours/week]
Capacity: unlimited
Min. number of students: unlimited
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Guarantor: doc. Mgr. Robert Šámal, Ph.D.
Class: Informatika Bc.
Informatika Mgr. - Matematická lingvistika
M Bc. MMIB > Povinné
M Bc. MMIB > 2. ročník
M Bc. MMIT > Povinné
Classification: Mathematics > Probability and Statistics
Incompatibility : NMAX059
Interchangeability : NMAX059
Is incompatible with: NMUE012, NMUE032, NSTP017, NSTP022, NSTP129, NSTP014, NSTP070, NSTP177, NMAX059
Is interchangeable with: NMAX059
Annotation -
Last update: doc. RNDr. Pavel Töpfer, CSc. (26.01.2018)
Basic lecture on Probability and Statistics for students of computer science. Students will learn the basic methods and concepts of the probabilistic description of reality: probability, random variable, distribution function and its density, random vectors, laws of large numbers. The emphasis will be on understanding the principles and the ability to use them. Students will also learn the basics of mathematical statistics with an emphasis on understanding the applicability and on practical usage using the R language.
Aim of the course -
Last update: G_M (05.06.2008)

The students will learn basics of the probability theory and mathematical statistics. The will be able to understand the core of stochastic procedures presented in other courses.

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.

S. Ross: A first course in probability, Pearson Prentice Hall, 2010.

R. Bartoszynski, M. Niewiadomska-Budaj: Probability and Statistical Inference, J. Wiley, 1996.

J. Anděl: Statistické metody, Matfyzpress, Praha 1998.

D. Jarušková: Matematická statistika, skriptum ČVUT, Praha 2000.

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

Teaching methods -
Last update: G_M (29.05.2008)


Requirements to the exam -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (11.10.2017)

The exam consists of two-parts written test. The computational part is closely related to the problems stated in the exercise classes. The theoretical part is based on the syllabus of the course modified according to the lectures in given semester. The final mark is then based on the results of both parts of the test.

In very rare situations the written test may be completed by oral part if a decision about the mark is needed.

Both parts of the test must be repeated if any part of the written test is failed.

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


Axioms of probability, basic examples (discrete and continuous). Conditional probability, the law of total probability, Bayes' theorem.

Random discrete variables: expectation, variance, linearity of expectation and its use. Basic discrete distributions.

Continuous random variables: description using probability density function. Basic continuous distributions.

Independent random variables. Random vectors (marginal distribution). Covariance, correlation.

Laws of large numbers, basic inequalities (Markov, Chebyshev, Chernoff), Central limit theorem.


Point estimates: unbiased estimates, confidence intervals.

Hypothesis testing, significance level. Two-sample tests.

Test of goodness of fit, test of independence.

Nonparametric estimates.

Bayesian and Frequentists Approach. Maximum a posteriori method, Least mean square estimate.

Maximum-likelyhood method. Bootstrap resampling.

Simulation, generation of random variables from a distribution. Monte Carlo simulation.

Informatively: Markov chains.

Entry requirements -
Last update: doc. RNDr. Daniel Hlubinka, Ph.D. (10.05.2018)

Knowledge required before enrollment:

combinatorics, basic formulas

calculus (sequences, series, integrals)

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