Question 3 Consider a system consisting of N components, all working independent of each other, and with life spans of each component exponentially distributed with mean \lambda ^(-1) . When a component breaks down, repair of the component starts immediately and independent of whether any other component has broken down. The repair time of each component is exponentially distributed with mean \mu ^(-1) . The system is in state n at time t if there are exactly n components under repair at time t . (3.1) Explain whether this is a birth and death process. (3.2) Determine the intensity matrix. (3.3) Find the stationary initial distribution. (3.4) Let \lambda =\mu and assume that all components are working. Find the distribution F(t) of the first time that two components do not work.