作者pushfish (听天使在呢喃)
看板Grad-ProbAsk
标题Re: [商管] [统计]-东吴98-商数(B组)-卜瓦松
时间Sat Oct 24 23:03:39 2009
※ 引述《pushfish (听天使在呢喃)》之铭言:
: ※ 引述《jackoyu (伟下列资料正确填写并回숩》之铭言:
: : An actuary determines that the numbers of major earthquake in certain area
: : follows Poisson distribution with mean 2 per year.
: : 1. whart is the probability that the inter-arrival time of two major
: : earthquakes is less than three months?
: : 2. what is the probability that there will be no major earthquakes in a year?
: : 3. counting the number of no major earthquake years in the next 10 years,
: : what is the probability that the count is two.
: : 4. counting the number of no major earthquake years in the next 100 years,
: : what is the probability that the count is over 15.
: : 题目如上述,是否可请各位大大帮忙解题,小弟一直苦无头绪,也不知如何下笔。
: : 看起来是卜瓦松过程,但还是不知要如何解题,也不太清楚题意,是否可以请各位
: : 赐教,谢谢!!
感谢pttjohn指正
1.第一题是问两个地震的间隔时间小於三个月
令Y为两地个之间隔时间 Y~EXP(入=2或B=1/2)
.25
P(Y<3/12)= S 2*e^-2xdx= 1-e^-0.5
0
2.一年内无地震
令X为1年地震个数 X~poi(入=2)
P(X=0)= e^-2
3. 题意为在十年内没有发生大地震的次数为两年
没有大地震为e^-2
令W为10年内发生大地震次数
P(W=2)=10C2 (e^-2)^2 (1-e^-2)^8
4. 100年内超过15次没有大地震
E(W)=100*e^-2 V(W)=E(W)*(1-e^-2)
接着藉由转成常态分配去算
P(W>15)===P(W>15.5) [连续校正]
P(Z>15.5-E(W) / S(W) )即为所求
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1F:推 pttjohn:正解! 10/27 15:25