An equivalent conjecture to Feige's Conjecture

Let X1, …, Xn be arbitrary non-negative independent random variables with respective expected values ${\mu }_i$ at most one. We sketch but do not prove an equivalent conjecture to Feige’s Conjecture $\mathbb{P}({\sum }_{i=1}^n{X}_i<\mu +1)\ge \exp (-1)$, where $\mu$ is the expected value of the sum of the random variables. We show by a simple example how this inequality finds use in mathematical finance.