Events, occuring according to a Poisson process with rate lamda, areregistered by a counter. However, each time an event is registeredthe counter becomes inoperative for the next b units of time and doesnot register any new events that might occur during that interval. R(t) denote the number of events that occur by time t and areregistered.
(a) Find the probability that the first k events are all registered.
(b) For t >= (n-1)b, find P{R(t) >= n}.