On some conjectures of Samuels and Feige
| Autor: | Paulin, Roland |
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| Rok vydání: | 2017 |
| Předmět: | |
| Druh dokumentu: | Working Paper |
| Popis: | Let $\mu_1 \ge \dotsc \ge \mu_n > 0$ and $\mu_1 + \dotsm + \mu_n = 1$. Let $X_1, \dotsc, X_n$ be independent non-negative random variables with $EX_1 = \dotsc = EX_n = 1$, and let $Z = \sum_{i=1}^n \mu_i X_i$. Let $M = \max_{1 \le i \le n} \mu_i = \mu_1$, and let $\delta > 0$ and $T = 1 + \delta$. Both Samuels and Feige formulated conjectures bounding the probability $P(Z < T)$ from above. We prove that Samuels' conjecture implies a conjecture of Feige. Comment: 4 pages |
| Databáze: | arXiv |
| Externí odkaz: |
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