Let \( X_1, X_2, \ldots \) be an infinite sequence of standard normal random variables which are not necessarily independent. Show that there exists a universal constant \( C \) such that \(\mathbb{E} \left[ \max_i \frac{|X_i|}{\sqrt{1 + \log i}} \right] \leq C\).

The best solution was submitted by 채지석 (수리과학과 석박통합과정, +4). Congratulations!

Here is the best solution of problem 2025-11.

Other solutions were submitted by 김동훈 (수리과학과 22학번, +3), 정서윤 (수리과학과 학사과정, +3), Anar Rzayev (수리과학과 19학번, +3).