probability 急

[匿名]

2010-10-30 7:49 am

Everett (“Solid Waste Transfer Station Design,” Journal of Environmental Engineering, 1995) uses the Poisson distribution to model the number of collection vehicles arriving at a station per hour. Suppose the collection vehicles arrive at an average rate of 3 per hour.

(i) Find the probability that exactly two collection vehicles arrive at the station in an
hour.

(ii) Let W be the time (in hour) between two successive arrivals of collection vehicles.
Find P(W > 0.5) .

更新1:

part ii 點解可以 take integral?

更新2:

part ii 點解用唔到poisson distribution計?

更新3:

未學過probability density function

回答 (1)

用戶9112

2010-10-30 8:33 am

✔ 最佳答案

===========================================================

圖片參考：http://img684.imageshack.us/img684/7946/78798226.png

2010-10-30 00:33:28 補充：
http://img684.imageshack.us/img684/7946/78798226.png

2010-10-30 00:42:24 補充：
Well, this is the basic in probability density function. The cumulative probability function is the integral of the probability density function. Have you ever learnt about it?
You can refer to wikipedia:
http://en.wikipedia.org/wiki/Probability_density_function

2010-10-30 09:16:12 補充：
Alternatively,
If W > 0.5, it means that within a period of 0.5 hour, there is no arrival of vehicle.
The probability of arrivals of vehicle within 0.5 hour is given by a Poisson distribution with λ = 0.5*3 = 1.5
The required probability = e^(-1.5) * (1.5^0) / 0! = 0.22313

👍 0 👎 0