We compute the probability mass function of the random variable which returns the smallest denominator of a reduced fraction in a randomly chosen real interval of radius $\delta$. As an application, we prove that the expected value of the smallest denominator is asymptotic, as $\delta\rightarrow 0$, to $(8\sqrt{2}/\pi^2)\delta^{-1/2}.$

翻译：我们计算随机变量的概率质量函数,该变量在随机选择的半径$\delta$的实际间隔中返回减少的分数的最小分母的最小分母。作为一个应用程序,我们证明最小分母的预期值为$\delta\rightrow 0$, 零美元为( 8\ sqrt{ 2}/\\pi\2)\delta\\\\\\\\ 1/2}$ 。