Chapter 13.1, Problem 29E

Show that each function defined as follows is a probability density function on the given interval; then the indicated probabilities.

$f\left(x\right)=\frac{1}{2}{\left(1+x\right)}^{-3/2};\left[0,\infty \right)$

a. $P\left(0\le X\le 2\right)$

b. $P\left(1\le X\le 3\right)$

c. $P\left(X\ge 5\right)$