Let {X(t), t ≥ 0} be a birth and death process for which
and let to > 0 be the time instant at which the first birth occurred.
(a) Suppose that we round off the time by taking the integer part. Calculate the probability that the first event from to will be a birth.
(b) What is the probability that there will be at least two births among the first three events from to?
(c) Calculate, if they exist, the limiting probabilities of the process.