Re: [機統] 一題與Poisson process有關的題目
※ 引述《ethan0221 (Ethan)》之銘言：
: 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)
a. 很簡單 (e^-0.2)^5 P(0)的五次方 =1/e
b. 10天水會沒有= 水<10000 units
5000+5000=10000
前面任何5天都能下雨不過只能下5000units
P(0)的9次方 = (e^-0.2)^9
*
P(1)= 0.8*0.2(e^-.2)
*
5
=5*0.2*0.8(e^-0.2)*(e^-.2)^9
加上
5天內就沒水 = 答案a
=>
1/e + (1/e)*0.8*(1/e)
※ 編輯: bambambam 來自: 98.196.117.239 (12/02 05:50)
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12/07 15:19, , 1F
12/07 15:19, 1F
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