Незалежність цифр $Q_2$-зображення випадкової величини з заданим розподілом
Let $\xi$ be a random variable with a given (uniform, exponential.) probability distribution on a segment $[0;1]$. We studyconditions for $Q_2$-digits $(\xi_n)$ of random variable$\xi=\Delta^{Q_2}_{\xi_1\xi_2...\xi_n...}$ to be independent. For $\xi$with exponential distribution, we prove that digit...
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| Datum: | 2019 |
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| Автори та афіліації: |
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| Ключові слова: | keywords |
| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
| Veröffentlicht: |
Інститут математики НАН України
2019
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| Online Zugang: | https://trim.imath.kiev.ua/index.php/trim/article/view/448 |
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| Назва журналу: | Transactions of Institute of Mathematics of NAS of Ukraine |
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Institution
Transactions of Institute of Mathematics of NAS of Ukraine| Zusammenfassung: | Let $\xi$ be a random variable with a given (uniform, exponential.) probability distribution on a segment $[0;1]$. We studyconditions for $Q_2$-digits $(\xi_n)$ of random variable$\xi=\Delta^{Q_2}_{\xi_1\xi_2...\xi_n...}$ to be independent. For $\xi$with exponential distribution, we prove that digits are independent ifand only if parameters $q_0$ and $q_1$ of this system ofrepresentation are equal to $\frac12$. Otherwise digits are dependentand this dependence is more complicated than Markov dependence. If the function of distribution of random variable with independent $Q_2$-digits has a positive derivative at all $Q_2$-binary points, then its distribution is uniform or exponential, moreover in the latter case the $Q_2$-representative is binary. |
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