Applied probability and stochastic process. please only answer if you are sure!

6.9. An electronic component works as follows: Electric impulses arrive to the com- ponent with exponentially distributed inter-arrival times such that the mean arrival rate of impulses is 90 per hour. An impulse is "stored" until the third impulse ar- rives, then the component "fires" and enters a "recovery" phase. If an impulse arrives while the component is in the recovery phase, it is ignored. The length of time that the component remains in the recovery phase is an exponential random variable with a mean time of one minute. After the recovery phase is over, the cycle is repeated; that is, the third arriving impulse will instantaneously fire the component. (a) Give the generator matrix for a Markov process model of the dynamics of this electronic component. (b) What is the long-run probability that the component is in the recovery phase? (c) How many times would you expect the component to fire each hour? 6.10. Consider the electronic devin 6.9. An electronic component works as follows: Electric impulses arrive to the com- ponent with exponentially distributed inter-arrival times such that the mean arrival rate of impulses is 90 per hour. An impulse is "stored" until the third impulse ar- rives, then the component "fires" and enters a "recovery" phase. If an impulse arrives while the component is in the recovery phase, it is ignored. The length of time that the component remains in the recovery phase is an exponential random variable with a mean time of one minute. After the recovery phase is over, the cycle is repeated; that is, the third arriving impulse will instantaneously fire the component. (a) Give the generator matrix for a Markov process model of the dynamics of this electronic component. (b) What is the long-run probability that the component is in the recovery phase? (c) How many times would you expect the component to fire each hour? 6.10. Consider the electronic devin