Čebyševova nerovnosť a jej varianty
| Thesis title in thesis language (Slovak): | Čebyševova nerovnosť a jej varianty |
|---|---|
| Thesis title in Czech: | Čebyševova nerovnost a její varianty |
| Thesis title in English: | Chebyschev type inequalities |
| Key words: | Čebyševova nerovnost|Chernoffovy nerovnosti|meze pro pravděpodobnosti odchylek|Hoeffdingova nerovnost|Bernsteinova nerovnost|Bennettova nerovnost |
| English key words: | Chebyschev inequality|Chernoff inequalities|probability of deviation bounds|Hoeffding inequality|Bernstein inequality|Bennett inequality |
| Academic year of topic announcement: | 2021/2022 |
| Thesis type: | Bachelor's thesis |
| Thesis language: | slovenština |
| Department: | Department of Probability and Mathematical Statistics (32-KPMS) |
| Supervisor: | doc. RNDr. Daniel Hlubinka, Ph.D. |
| Author: | hidden - assigned and confirmed by the Study Dept. |
| Date of registration: | 16.11.2021 |
| Date of assignment: | 18.11.2021 |
| Confirmed by Study dept. on: | 02.12.2021 |
| Date and time of defence: | 30.01.2023 08:00 |
| Date of electronic submission: | 05.01.2023 |
| Date of submission of printed version: | 09.01.2023 |
| Date of proceeded defence: | 30.01.2023 |
| Opponents: | doc. Ing. Marek Omelka, Ph.D. |
| Guidelines |
| Student se seznámí s Čebyševovou nerovností a Chernoffovými nerovnostmi. Na jejich základě se zaměří na další nerovnosti tohoto typu včetně odvození dolních mezí pro pravděpodobnost odchylek. Výsledky porovná s nerovnostmi odvozenými z centrální limitní věty. |
| References |
| Wassily Hoeffding. Probability inequalities for the sum of bounded random variables. Journal of theAmerican Statisitcal Association, 58:13–30, 1963.
Michael Mitzenmacher and Eli Upfal. Probability and Computing: Randomized Algorithms and Probabilisitic Analysis. Cambridge University Press, 2005. Herman Chernoff. A measure of asymptotic efficiency for tests of hypothesis based on the sum of observations. Annals of Mathematical Statistics, 23:493–509, 1952. |