中文摘要：

首先,探讨了取自区间[0,1],服从某种概率分布的随机样本点的极差期望。其次,利用凸性概念推导出了极差期望的一个上界,而且它对所有可能的这种概率分布都有效.最后,证明了对于此上界,仅有一个概率分布可以达到。

英文摘要：

Firstly,the papers investigate the range expectation of a random variable in [0,1] from a certain probability distribution. Secondly,deduce an upper bound of the range expectation by the convexity definition,which is viable to all probability distribution. Finally,prove that the upper bound have only a probability distribution can be achieved.