(Solved): The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a perio ...

The total number of hours, in units of 100 hours, that a family runs a vacuum cleaner over a period of one year is a random variable \( \mathrm{X} \) having the density function shown to the right. Find the variance of \( X \). \[ f(x)=\left\{\begin{array}{cc} \left(\frac{1}{9}\right)(x-4), & 4