Solution
= Solution
{c}
For $0\le t\le1$, <independence> and the <uniform distribution> give
$$
\mathbb P\left(\frac M\theta\le t\right)=\mathbb P(X_1\le\theta t,\ldots,X_n\le\theta t)=t^n.
$$
Therefore the <cumulative distribution function> is
$$
\boxed{F_{M/\theta}(t)=\begin{cases}0,&t<0,\\t^n,&0\le t\le1,\\1,&t>1.\end{cases}}
$$
It contains no $\theta$, so $M/\theta$ is a <pivotal quantity>.