Let $U_{1},...,U_{n}$ be $n$ independent standard uniform random variables. In this paper, it's shown that if $(\lambda_{1}^{2}, ....,\lambda_{n}^{2}) \mathop \le \limits^m ({\lambda_{1}^{*}}^{2},...,{ \lambda_{n}^{*}}^{2})$, then $\sum_{i=1}^{n}\lambda_{i}U_{i}$ is greater than $\sum_{i=1}^{n}\lambda_{i}^{*}U_{i}$ in the usual stochastic order, where $\lambda_{1},...,\lambda_{n}$ $(\lambda_{1}^{*},...,\lambda_{n}^{*})$ are positive real values.
