2. Events, occurring according to a renewal process {N(t) : t 2 0} with mean inter-renewal time , are registered by a counter. Each time an event is registered, the counter becomes inoperative for the next b units of time and does not register any new events that might occur during that time interval. Let R(t) denote the number of events that are registered by time t, and 5, denote the duration between two registered events. (a) Assume that an event occurs and is registered at time 0. Is {R(t) : t 2 0} a renewal process and why? [Hint: express 5, via SN(t)] (b) Let m(t) represent the mean value function of {N(t) : t 2 0} and assume that it is known. Compute lim,- c E[R(t)]/t