After being repaired, a machine functions for an exponential time with mean 20 hours and then fails. Upon failure, a repair process begins with 3 stages. Each stage lasts and exponential amount of time with mean 0.1 hours. Each repair stage will end successfully with probability 0.7 and unsuccessfully with probability 0.3. When a repair stage ends successfully, we move into the next repair stage (or the machine is completely repaired if we just successfully completed stage 3 repair). When a repair stage ends unsuccessfully, with will have to start the repair process over in stage 1. The status of the machine can be modeled as a continuous-time Markov chain with states 0 (= working), 1 (= stage 1 repair), 2 (= stage 2 repair), 3 (= stage 3 repair).1) Give parameters for the continuous Markov-chain. STATES 0 1 2 3P= 1 ? ? ? 2 ? ? ? 3 ? ? ?2) Find limiting probabilities P0, P1, P2, P3.3) What proportion of the time is the machine functional?