面经 Cornell MFE （Sasha）[2011-03-23]
作者：happyha23
日期：2011-03-25
昨天晚上面的，因为后来电脑没电了，早晨受到他家的Ad，现在分享下面经：
Sasha 面的，两个问题
1. why MFE?
2. 投硬币，第一次出现连续两投出个head所需投掷次数的期望。
之后是我问他Cornell 和哥大相比的优势，然后聊了几句后他还问了问现在还有哪些学校的ad，deadline是什么。
一共20分钟多一点，Sasha人很好，有点口音但也还挺容易听懂的，祝大家好运~~
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Mark第二个问题
Let a = expected number of throws to first head.
We must make 1 throw at least and we have probability 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 consecutive heads.
Consider that we have just thrown a head and what happens on the next
throw. We are dealing with the (a + 1)th throw, 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.
写个程序，模拟10000遍，取第一次得到2个head抛掷次数的平均值，当作近似解~