Solution
= Solution
Integrating the <probability density function> from its lower endpoint to $x$ gives the <cumulative distribution function>
$$
\boxed{F(x)=\begin{cases}0,&x\leq1,\\1-x^{-\alpha},&x>1.\end{cases}}
$$
It is continuous and strictly increasing on the support. Hence the unique <median> $m$ satisfies $F(m)=1/2$, or $m^{-\alpha}=1/2$. Therefore
$$
\boxed{m=2^{1/\alpha}}.
$$