Chapter 9.2, Problem 24E

(a)

To determine

The probability $P\left(0<x<2\right)$, for the probability density function $f\left(x\right)=\frac{5}{4{\left(x+1\right)}^2}$ over the interval $\left[0,4\right]$

(b)

To determine

The probability $P\left(2<x<4\right)$, for the probability density function $f\left(x\right)=\frac{5}{4{\left(x+1\right)}^2}$ over the interval $\left[0,4\right]$.

(c)

To determine

The probability $P\left(1<x<3\right)$, for the probability density function $f\left(x\right)=\frac{5}{4{\left(x+1\right)}^2}$ over the interval $\left[0,4\right]$.

(d)

To determine

The probability $P\left(x\le 3\right)$, for the probability density function $f\left(x\right)=\frac{5}{4{\left(x+1\right)}^2}$ over the interval $\left[0,4\right]$.