The water level of a certain reservoir is depleted at a constant rate of 1000 units daily. The reservoir is re?lled by randomly occurring rainfalls. Rainfalls occur according to a Poisson process with rate 0.2 per day. The amount of water added to the reservoir by a rainfall is 5000 units with probability 0.8 or 8000 units with probability 0.2. The present water level is just slightly below 5000 units.
(a) What is the probability the reservoir will be empty after ?ve days?
(b) What is the probability the reservoir will be empty sometime within the next ten days?