Re: [問題] 問一題順序統計
※ 引述《unbiased (unbiased)》之銘言：
: Let Y1<Y2<Y3...<Y9<Y10 be the order statistics of a random sample
: of size 10 from a distribution of the continuous type having distribution
: function F(x).
: Find (a)What is the distribution of U=1-F(Y3)?
: (b)What is the distribution of V=F(Y10)-F(Y5)+F(Y2)-F(Y1)?
F(x_i)->U(0,1) and F(x) is nondecreasing
s.t F(Y3)=F(x_i)中第3小 且 F(x_i)->U(0,1)
thus F(Y3)->beta(3,8) 同理 F(Y10)->beta(10,1)
F(Y5)->beta(5,6)
F(Y2)->beta(2,9)
F(Y1)->beta(1,10)
(a)let U=1-X X->beta(3,8)
X=1-U |J|=1
Γ(11) 2 7
fu(u)=fx(1-u)=----------(1-u)(u) -> beta(8,3)
Γ(3)Γ(8)
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◆ From: 220.143.152.2
※ 編輯: mangogogo 來自: 220.143.152.2 (02/15 21:49)
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02/16 18:48, , 1F
02/16 18:48, 1F
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