掰玉米问题，The Marriage Problem

（ZT)假设玉米长度的分布是已知正态分布 (mu = 1 ft, sigma = 0.3 ft)，地里一共有１００个玉米，一个一个看, 每看一个玉米，当时就要决定要不要掰了带走（没掰的不能再回头掰哦）。一共可以掰走最多５个玉米。

如何掰，能使的带走的玉米总长度最大。

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这样思路对吗？
2选一，we know that n1, n2, i.i.d normal. Our goal is to choose n1=m if P(m > n2) > 0.5. otherwise, choose n2.

With P(m > n2) > 0.5 , m can be found numerically by looking into erfc table.

3选二，we know that n1, n2, n3, i.i.d normal.
- If we choose n1=m1, we will choose n2=m2 if P(m2 > n3) > 0.5. This is the same as 2选一.
- We shall choose n1=m1 if P(m1 < n2 and m1 < n3) < 0.5. otherwise choose n2 and n3.
With i.i.d, P(m1 < n2 and m1 < n3) = P(m1 < n_i)^2 < 0.5. Thus, we will pick n1 = m1 when P(m1 < n_i) < \sqrt(0.5) ~0.36.
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The Marriage Problem

http://www.americanscientist.org/issues/issue.aspx?id=5783&y=0&no=&content=true&page=2&css=print