A truck water pump failures have been analyzed and it has been found that the pump failure is random, but a function of its age (in days). Data on 2000 failures have been collected. Using a statistical goodness-oft test, the cumulative density function of pump failure times is plotted as below: F(t) 1.0 0.6 30 40 80 (a) Write the cumulative density function (CDF), the probability density function (pdf), and the reliability function (R(t)) for the pump. (b) Find the mean time to failure of the component