Textbook Problem

Demand The weekly demand x (in tons) for a certain product is described by the probability density function

$f\left(x\right)=\frac{1}{36}x{e}^{-x/6},\left[0,\infty \right]$

Find and interpret each probability.

$\begin{array}{l}\left(\text{a}\right)P(x<6)\hfill \\ \left(\text{b}\right)P(6<x<12)\hfill \\ \left(\text{c}\right) P(12\le x\le 24)\hfill \\ \left(\text{d}\right)P(x>12)=1-P(x\le 12)\hfill \end{array}$