[問題] 請幫忙看看這個推導有沒有問題
題目:X_n i.i.d r.v's 證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
請幫忙看看@@"
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※ 編輯: wulingking 來自: 218.173.168.178 (10/18 22:17)
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