MATHS M1 - Ans.fyi 參考答案

MATHS M1

ddobtn

2012-09-24 3:15 am

Mr Liu found that the number of cars passing his house between 8:00 am and 9:00 am on a weekday follows a Poisson distribution with a parameter of 3.4.

(a) Find the probability that the number of cars passing his house between 8:00 am and 9:00 am on a particular weekday is at least 4.

(b) Find the probability that no cars pass his house between 8:00 am and 9:00 am on a particular weekday.

(c) Find the probability that in a period of 100 days , there are two days during which no cars pass Mr Liu's house between 8:00 am and 9:00 am

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回答 (1)

用戶10012

2012-09-24 6:06 am

✔ 最佳答案

(a) Let X = no. of car passing between 8 to 9 am.
So P(at least 4 cars passing between 8 to 9 am) =
P(X > = 4) = 1 - P(X < 4) = 1 - P(X = 0) - P(X = 1) - P(X = 2) - P(X = 3)
= 1 - e^(-3.4) - 3.4e^(-3.4) - (3.4)^2e^(-3.4)/2 - (3.4)^3e^(-3.4)/6 =
= 1 - e^(-3.4)[1 + 3.4 + 5.78 + 6.55] = 0.4417
(b) No car passing = P(X = 0) = e^(-3.4) = 0.03337
(c) Let Y = No. of days with no car passing out of 100 days. That is n = 100, p = 0.03337
So Y ~ B(100, 0.03337)
P(2 days with no cars passing) = P(Y = 2) = (100C2)(0.03337^2)(1 - 0.03337)^98
= 50 x 99 x 0.001113557 x 0.035934 = 0.19807 = 0.1981.

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