1. Events occur according to a Poisson process. Suppose that the expected number of occurrences per hour is 3, and let Tn denote time in hours of the nth occurrence. Find the expected value and variance of T3 given that the first occurrence was at time 1 and the second occurrence was at time 2.
2. In a Poisson process, the probability is 0.60 that after an occurrence of the event, it will take at least 2 months until the next event. Find the probability that exactly four claims will occur within any 5-month period.