Re: [問題] 分佈收斂
Since {X_n}, {Y_n} are independent, (X_n,Y_n) converges to (X,Y) weakly
(it's obvious from the two dimensional characteristic function).
From the continuous mapping theorm (R^2->R^1), you can get X_n*Y_n converges
weakly to XY, where X and Y are random variables whose distribution are
F and G respectively.
※ 引述《wulingking (等的好辛苦)》之銘言：
: X_n,Y_n相互獨立且c.d.f為F_n,G_n
: 又F_n,G_n分佈收斂到F,G證F_nG_n分佈收斂到FG
: 想法:因c.d.f.在0,1間...極限一定存在
: 故limF_nG_n=limF_n limG_n=FG
: 又覺得怪怪的@@
: 請問有問題嗎
: 謝謝~
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推
10/19 23:34, , 1F
10/19 23:34, 1F
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10/20 03:33, , 2F
10/20 03:33, 2F
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10/20 03:33, , 3F
10/20 03:33, 3F
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10/20 03:33, , 4F
10/20 03:33, 4F
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10/20 21:30, , 5F
10/20 21:30, 5F
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