Initially, at time = 0, a Poisson process is set to produce on the average one incident per unit time. It is observed for a time T and incidents occur at t, 1, ..., . It is then learnt from other information that at time T the Poisson process is working at a rate of two incidents per unit time. If it is believed that the process doubled its rate at some instant of time, 0, between 0 and T and that is equally likely to be anywhere in (0, T), discuss the form of the posterior distribution of given the observed pattern of incidents in (0, 7).