3.3. Pulses arrive at a counter according to a Poisson process of rate A.

All physically realizable counters are imperfect, incapable of detecting all signals that enter their detection chambers. After a particle or signal arrives, a counter must recuperate, or renew itself, in preparation for the next arrival. Signals arriving during the readjustment period, called dead time or locked time, are lost. We must distinguish between the arriving particles and the recorded particles. The experimenter observes only the particles recorded; from this observation he desires to infer the properties of the arrival process.

Suppose that each arriving pulse locks the counter for a fixed time T.

Determine the probability p(t) that the counter is free at time t.