作者kanebo998 (无情的雨)
看板Statistics
标题Re: [问题] 请教一题统计的问题：
时间Tue Feb 2 00:16:43 2010
先定事件:
会倒债:D 良好评价:F
c c
不会倒债:D 不良的评价:F
※ 引述《jeffho (yeungwailei)》之铭言：
: A customer has approached a bank for a loan. From the past experience, the
: bank believes there is a 10% chance that the customer will default on the
可知P(D)=0.1
: loan. The bank can run a credit check on the customer. The credit check will
: yield either a favorable or an unfavorable report. Historical information
: shows that for those default customers, favorable reports were received 1 out
: of 50 of the time. On the other hand, for those customers that were not default,
P(F|D)=0.02
: favorable reports were received 95 out of 100 of the time. If a favorable report
c
且P(F|D )=0.95
: is received, what is the probability (to 4 decimal places) that the customer
: will default on the loan?
: {Hint: Construct a contingent table of the above problem first.}
: 小弟粗略翻译了一下中文意思大概是这样：
: 一个顾客去问银行借钱，根据过去经验，银行认为这家伙有10%机会不还钱。
: 银行可以给这人客做一个信用评估，然後这个评估会产生一个好的或是一个不好的报告，
: 以过去的数据统计出，对於那些会逃债的人客。他们每50个报告只有1个是好的报告，
: 而不会逃债的，是每100个报告有95个都是好的，现在我们对这位客人做信用评估，
: 那麽请问如果他得出一个好的报告，他结果会逃债的机率是多少？
所求为P(D|F)
先划出树状图:
c
F ---D 因为P(D) = 0.1 => P(D ) = 0.9
\
\ c 又 P(F|D) = 0.02 = P(F交D)/P(D) => P(F交D) = 0.002
D
c c c c
且 P(F|D ) = 0.95 = P(F交D )/P(D ) => P(F交D ) = 0.855
c c
F ---D 所以P(F) = P(F交D) + P(F交D ) = 0.857
\
\ c
D 而所求P(D|F) = P(D交F) / P(F) = 0.002/0.857 = 0.0023
#
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1F：推 jeffho:谢谢解答...我先洗个澡清醒一下再钻研^^" 02/02 00:42
2F：推 jeffho:完全弄明白了T_T 明天要交功课呢，谢谢你，你是我的救星>< 02/02 01:23
3F：→ kanebo998:不客气 取之於网路 回馈於网路 02/02 12:17