4.2. A system is subject to failures. Each failure requires a repair time that is exponentially distributed with rate parameter

a. The operating time of the system until the next failure is exponentially distributed with rate parameter /3. The repair times and the operating times are all statistically independent. Suppose that the system is operating at time 0. Using equation

(4.5), determine an approximate expression for the mean number of failures up to time t, the approximation holding for t >> 0.