MathDB

Miklós Schweitzer 2008, Problem 11

Source: Miklós Schweitzer 2008

July 30, 2016

Miklos Schweitzercollege contestsnormal distributionprobability

Problem Statement

Let

\zeta_1, \ldots, \zeta_n

be (not necessarily independent) random variables with normal distribution for which

E\zeta_j=0

and

E\zeta_j^2\le 1

for all

1\le j\le n

. Prove that

E\left( \max_{1\le j\le n} \zeta_j \right)\le\sqrt{2\log n}

(translated by Miklós Maróti)