Solution
= Solution
Normalization gives $c=8/3$. Integrating the <probability density> from one to two gives
$$
\mathbb P(X\leq2)=\frac83\int_1^2x^{-3}\,\mathrm dx-\int_1^2x^{-4}\,\mathrm dx=\frac83\frac38-\frac7{24}=\boxed{\frac{17}{24}}.
$$
The <expected value> exists, since the first-moment integrals converge, and equals
$$
\mathbb E X=\frac83\int_1^\infty x^{-2}\,\mathrm dx-\int_1^\infty x^{-3}\,\mathrm dx=\frac83-\frac12=\boxed{\frac{13}{6}}.
$$