# 18.S096: An extra Open Problem

I have just added an extra open problem (4.6.) to the fourth set of lecture notes. I am documenting it here.

Prove or disprove the following conjecture by Feige:

Given $n$ independent random variables $X_1,\dots,X_n$ s.t., for all $i$, $X_i \geq 0$ and $\mathbb{E} X_i = 1$ we have

$\mathrm{Prob}\left( \sum_{i=1}^n X_i \geq n+1 \right) \leq 1 - e^{-1}$.