ČESKÉ VYSOKÉ UČENÍ TECHNICKÉ V PRAZE
STUDIJNÍ PLÁNY
2023/2024

# Probability and Statistics

Kód Zakončení Kredity Rozsah Jazyk výuky
BIE-PST.21 Z,ZK 5 2P+2C anglicky
Garant předmětu:
Pavel Hrabák
Přednášející:
Francesco Dolce, Pavel Hrabák, Petr Novák
Cvičící:
Francesco Dolce, Pavel Hrabák, Petr Novák
Předmět zajišťuje:
katedra aplikované matematiky
Anotace:

Students will learn the basics of probabilistic thinking, the ability to synthesize prior and posterior information and learn to work with random variables. They will be able to apply basic models of random variable distributions and solve applied probabilistic problems in informatics and computer science. Using the statistical induction they will be able to perform estimations of unknown distributional parameters from random sample characteristics. They will also be introduced to the methods for testing statistical hypotheses and determining the statistical dependence of two or more random variables.

Basics of combinatorics and mathematical analysis.

Osnova přednášek:

1. Probability - random events, event space structure, probability of a random event and its basic properties.

2. Conditional probability - dependent and independent events, Bayes theorem.

3. Random variables - distribution function of a random variable, continuous and discrete distributions, quantiles, median.

4. Characteristics of random variables - expected value, variance, general moments, kurtosis and skewness.

5. Overview of basic distributions - binomial, geometric, Poisson, uniform, normal, exponential. Their basic properties.

6. Random vectors - joint and marginal statistics, correlation coefficient, dependence and independence of random variables.

7. Random vectors - conditional distributions, sums of random variables.

8. Limit theorems - laws of large numbers, central limit theorem.

9. Statistical estimation - classification and processing of data sets, graphical representation of data, random sample, point estimation, basic sample statistics, sample mean and variance.

10. Interval estimation - confidence intervals for expectation and variance.

11. Hypothesis testing - testing strategy, tests for expectation and variance, their modifications.

12. Application of statistical testing in computer science.

13. Correlation and regression analysis: Linear and quadratic regression, sample correlation.

Osnova cvičení:

1. Basics of probability.

2. Conditional probability.

3. Random variables.

4. Basic characteristics of random variables.

5. Using basic distributions.

6. Random vectors - independence, covariance.

7. Random vectors - conditional distributions and sums.

8. Limit theorems

9. Processing of sets of data.

10. Statistical point estimation.

11. Interval estimation.

12. Hypotheses testing.

13. Regression and correlation analysis.

Cíle studia:

The goal of the module is to introduce the students to basics of probability theory and mathematical statistics while focusing on applications in informatics.

Studijní materiály:

1. Ahn H. : Probability and Statistics for Science and Engineering with Examples in R. Cognella, 2017. ISBN 978-1516513987.

2. Johnson J. L. : Probability and Statistics for Computer Science. Wiley-Interscience, 2008. ISBN 470383429.

3. Bonselet Ch. : Probability, Statistics, and Random Signals. Oxford University Press, 2016. ISBN 978-0190200510.

4. Grimmett G. R., Stirzaker D. R. : Probability and Random Processes (3rd Edition). Oxford University Press, 2001. ISBN 0-19-857223-9.

Poznámka:

Chybí klíčvá slova a webová stránka.

Rozvrh na zimní semestr 2023/2024:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 místnost T9:347Dolce F.09:15–10:45(přednášková par. 1)DejviceNBFIT učebnamístnost T9:347Dolce F.16:15–17:45(přednášková par. 1paralelka 101)DejviceNBFIT učebna
Rozvrh na letní semestr 2023/2024:
Rozvrh není připraven
Předmět je součástí následujících studijních plánů:
Platnost dat k 30. 8. 2023
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/cs/predmet6699306.html