Chapter 12.2, Problem 38E

(a)

To determine

Whether $f(x)=2{\left(x+1\right)}^{-3}$ is a probability density function for $x\ge 0$ or not.

(b)

To determine

The cumulative distribution function of F(x) for density function $f(x)=2{\left(x+1\right)}^{-3}$, $x\ge 0$.

(c)

To determine

The $\mathrm{Pr}\left(1\le x\le 2\right)$ and $\mathrm{Pr}\left(3\le X\right)$.