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11

Part of 2008 Miklós Schweitzer

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Miklós Schweitzer 2008, Problem 11

Source: Miklós Schweitzer 2008

7/30/2016
Let ζ1,…,ζn\zeta_1, \ldots, \zeta_n be (not necessarily independent) random variables with normal distribution for which Eζj=0E\zeta_j=0 and Eζj2≤1E\zeta_j^2\le 1 for all 1≤j≤n1\le j\le n. Prove that E(max⁡1≤j≤nζj)≤2log⁡nE\left( \max_{1\le j\le n} \zeta_j \right)\le\sqrt{2\log n}
(translated by Miklós Maróti)
Miklos Schweitzercollege contestsnormal distributionprobability