Solution
= Solution
A <probability density function> must be nonnegative and integrate to one. For $c>0$,
$$
\int_1^\infty c x^{-c-1}\,dx
=\left[-x^{-c}\right]_1^\infty=1.
$$
At $c=0$ the function is identically zero, while $c<0$ makes it negative on $x>1$. Thus $\boxed{c>0}$ is necessary and sufficient. The resulting law is a <Pareto distribution> with scale one and shape $c$.