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Course, academic year 2023/2024
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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 2023
Semester: summer
E-Credits: 5
Hours per week, examination: summer s.:2/2, C+Ex [HT]
Capacity: unlimited
Min. number of students: unlimited
4EU+: no
Virtual mobility / capacity: no
State of the course: taught
Language: Czech, English
Teaching methods: full-time
Teaching methods: full-time
Additional information:
Guarantor: doc. Mgr. Robert Šámal, Ph.D.
Mykhaylo Tyomkyn, 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 -
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.
Last update: Töpfer Pavel, doc. RNDr., CSc. (26.01.2018)
Aim of the course -

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.

Last update: G_M (05.06.2008)
Course completion requirements -

The credit will be given for active participation in tutorials, quizzes, homework, 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 semi-oral. Obtaining the credit is necessary before the final exam.

Last update: Feldmann Andreas Emil, doc., Dr. (09.02.2022)
Literature -

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.

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


Last update: G_M (29.05.2008)
Requirements to the exam -

The exam is semi-oral, which means that each student will get some questions about to the content of the lecture. After getting some time to prepare, each student will explain their answers to the teacher and the grade is determined by their performance. Each student will get questions on each of the two parts of the lecture (probability theory and statistics).

In exceptional cases the exam can be taken online.

Last update: Feldmann Andreas Emil, doc., Dr. (09.02.2022)
Syllabus -


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-likelihood method. Bootstrap resampling.

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

Informatively: Markov chains.

Last update: Šámal Robert, doc. Mgr., Ph.D. (27.01.2022)
Entry requirements -

Knowledge required before enrollment:

combinatorics, basic formulas

calculus (sequences, series, integrals)

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