[機統] 一題與Poisson process有關的題目
懇請大家幫忙><
The water level of a certain reservoir is depleted at a constant rate of
1000 units daily.
The reservoir is refilled 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 5 days?
(b) What is the probability the reservoir will be empty sometime within the
next ten days?
參考答案應該是: (a) 1/e (b) 1/e + (1/e)*(0.8)*(1/e)
不知道是怎麼算的...
請大家幫忙，非常謝謝!! :]
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