[問題] 請幫忙看看這個推導有沒有問題

[wulingking (等的好辛苦)]

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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◆ From: 218.173.168.178
※ 編輯: wulingking      來自: 218.173.168.178      (10/18 22:17)
→ clickhere:你的 iff 方向反了. if 是 <=, only if 是 =>
→ clickhere:the number of n such that |X_n|>n is finite??
→ clickhere:你是要說P(|X_n|>n)<epsilon?
→ clickhere:我相大概是對的. 期望值等於右尾機率和.
→ clickhere:如果右尾太厚了, 那期望值很難有機會finite.