1. a) Consider a renewal process that brings a component to as good as new state after each repair. The failure and repair times are iid and follow their respective distributions. The pdf of this process is given by the convolution of u(t) and rm, where t) and g(t) are the failure and repair distributions of the component. The pdf, t) of the process can be determined through the Laplace transform, ftt) = u(t)r{t) and its Laplace invert. A producer of motor, puts a DC motor to a reliability test by stressing it to a continuous load and get it repaired immediately post failure to restore it to initial condition. The test continues with this procedure of failure and repair cycles. The failure and repair distributions of this motor are exponential with rates 6 x 105 failures per hour and 4x10'2repairs per hour, respectively. Using the Laplace Transform approach, determine the expected number of motor failures in (0,2 x104) hours