[機統] strong law of large number消失

看板Math作者時間13年前 (2012/07/18 18:19), 編輯推噓1(1推 0噓 5→)
留言6則, 3人參與, 最新討論串1/1
Let X_0 is random variable from U[0,1] , for n≧1 X_n+1 has uniform distribition on [0, X_n] show that ( log X_n )/ n converges a.s 我的做法 let Y_0 = X_0 , Y_n = X_n /X_n-1 for n≧1 then Y_n is i.i.d U[0,1] we can rewrite log X_n / n = Σ log Y_n / n since X_n = Y_0 * Y_1 * ... *Y_n Σ log Y_n / n 這裏我想用 stong law of large number 但是 E(log Y_1 ) 是不收斂的 where Y_1 ～U[0,1] 想請教是哪裡做錯了嗎 感謝 -- ※ 發信站: 批踢踢實業坊(ptt.cc)
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07/18 21:46, , 1F
E[log Y_1] 不是 -1 嗎？還有那樣取 Y_i 不一定獨立
07/18 21:46, 1F
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07/19 07:59, , 2F
抱歉 可以請教有甚麼更好的做法嗎
07/19 07:59, 2F
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07/20 01:29, , 3F
I think that the Y_n are iid U(0,1) is implied
07/20 01:29, 3F
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07/20 10:53, , 4F
所以可以用law of large number 囉 ??
07/20 10:53, 4F
推
07/20 10:58, , 5F
可以
07/20 10:58, 5F
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07/20 13:44, , 6F
感謝m(_ _)m
07/20 13:44, 6F
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