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b***k 发帖数: 2673 | 1 ☆─────────────────────────────────────☆
Ithink (牛夫人) 于 (Mon Apr 27 20:21:20 2009) 提到:
假设有n个uniform random variable from [0,1],那么他们的min and max的
expectation是什么?
min应该是1/(n+1),但不知道怎么证明。。。
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daj (肉丝炒饭--小吵肉fan) 于 (Mon Apr 27 20:48:13 2009) 提到:
那n个是 independent
P(min
get density function for u
then, get mean
这个还挺流行的, one of my on site interview question
不过 ask for max
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zzrays (时代男保姆) 于 (T | N**k 发帖数: 16 | 2 E(Min(X_k, k=1 to n)=Sum_(i=1to n)X_i*P(X_k > X_i, all k!=i)
by symmetry it is
n*X_i*P(X_k > X_i, all k!=i)
=n*Int_0to1(x*(1-x)^(n-1))dx = 1/(n+1)
E(Max) = n/(n+1) same argument. |
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