Cornell MFE 面筋一枚 [2011-04-04]
作者：gaowei1988
日期：2011-04-05
Cornell MFE 面筋一枚
虽然都这时候了估计用处不大，就算留点史料吧。
1. 对于financial crysis的看法，原因和处理方法（完全没料到。。。）
2. 抛硬币，期望几次可以有1个正面，期望几次有连续两正面
3. 两人在一圆桌上放硬币（不能叠在别人放的硬币上）最后放不下的人输，问你的策略
就这仨题，别的嘛没问。
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自己答得很挫，因为完全没准备。这个问题网上能找到的资料太多了吧
建议你有空读一下Restoring financial stability--Viral V.Acharya & Matthew Richardson
见LSLSLS
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第一题开放啊，自圆其说就好
第二题借前人帖子一用
found online
Let a = expected number of throws to first head.
We must make 1 throw at least and we haveprobability 1/2 of a head
and probability 1/2 of returning to a, so
a = (1/2)1 + (1/2)(1 + a)
(1/2)a = 1
a = 2.
Let E = expected number of throws to 2 consecutiveheads.
Consider that we have just thrown a head and whathappens on the next
throw. We are dealing with the (a + 1)ththrow, with probability 1/2
this is not a head and we return to E.
So E = (1/2)(a + 1) + (1/2)(a + 1 + E)
(1/2)E = a + 1
E = 2(a + 1)
and now putting in the value a = 2 we get E= 2(3) = 6
Expected throws to 2 consecutive heads is 6.
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[/quote]
见LSLSLS
[/quote]
见LSLSLS
正解
smart！