面经 Cornell MFE （Sasha）[2011-03-23]

happyha23

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~~

receptive

cong~~

yucca007

LZ我表示第2题不会做啊。。。

zjuer2007

LZ我表示第2题不会做啊。。。

-- by 会员 yucca007 (2011/3/24 13:25:20)

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~

zhaopenglu

found online

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.

poolish

递归
E = 1/2 * (1+E) + 1/4 * (2+E) + 1/4 * 2
详见http://www.guokr.com/post/456271/

syeira

我是来马克第二个问题的。。。

周俱清

Mark一下！               

天婧杀

Mark第二个问题

iris_ren

mark一下第二个问题...感谢楼主