We consider a pure birth process for which, when there are n individuals in the population, the average time (in hours) needed for a birth to occur is equal to 1/n, for n > 0. (a) Knowing that at time...

We consider a pure birth process for which, when there are
n
individuals in the population, the average time (in hours) needed for a birth to occur is equal to 1/n, for n > 0.

(a) Knowing that at time
t
there are two individuals in the population and that at time t + 1 there are still two, what is the probability that the next birth will take place between t + 2 and t + 3?

(b) If, at the origin, the population is composed of a single individual, what is the probability that there will be exactly four births during the first two hours?