Chapter 3.3, Problem 7E

The total number of hours, measured in units of100 hours, that a family runs a vacuum cleaner over aperiod of one year is a continuous random variable Xthat has the density function

   $f\left(x\right)=\{\begin{array}{c}x,0<x<1,\\ 2-x,1\le x<2,\\ 0,\text{ elsewhere}.\end{array}$

Find the probability that over a period of one year, afamily runs their vacuum cleaner

1. less than 120 hours;
2. between 50 and 100 hours.