Solution
= Solution
Call the normalization constant $K$ to distinguish it from the moment index used later. A <probability density function> must have total <integral> one, so
$$
1=K\int_c^\infty x^{-\theta-1}\,dx=\frac{Kc^{-\theta}}\theta.
$$
Therefore \b[$K=\theta c^\theta$], the value denoted $k$ in the density. This is the <Pareto distribution> with scale $c$ and shape $\theta$.