作者wulingking (等的好辛苦)
看板Statistics
标题[问题] 请帮忙看看这个推导有没有问题
时间Sat Oct 18 22:10:21 2008
题目:X_n i.i.d r.v's 证E(|X_1|)<∞ if and only if P(|X_n|>n,i.o.)=0
想法:
(If)
Let E(|X_1|)=b<∞ exists N_0 such that
|X_n|<n for n>=N_0
if and only if ΣP(|X_n|>n)<∞
then P(|X_n|>n,i.o.)=0
(Only if)
P(|X_n|>n,i.o.)=0
the number of n such that |X_n|>n is finite
=>E(|X_n|)<∞ and X_n i.i.d=>done
请帮忙看看@@"
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※ 编辑: wulingking 来自: 218.173.168.178 (10/18 22:17)
1F：→ clickhere:你的 iff 方向反了. if 是 <=, only if 是 => 10/19 03:51
2F：→ clickhere:the number of n such that |X_n|>n is finite?? 10/19 03:52
3F：→ clickhere:你是要说P(|X_n|>n)<epsilon? 10/19 03:52
4F：→ clickhere:我相大概是对的. 期望值等於右尾机率和. 10/19 03:53
5F：→ clickhere:如果右尾太厚了, 那期望值很难有机会finite. 10/19 03:54