Let Y1<Y2<...<Y10 be the order statistics of a random sample
of size 10 from a distribution of the continuous type having
distribution function F(x). Determine the distribution of V
= F(Y10)-F(Y5)+F(Y2)-F(Y1)
iid
這一題因為F(X1),F(X2),...,F(X10)----->Uni(0,1)
所以F(Y1),F(Y2),...,F(Y10)很好找
所以我就從F(Y10),F(Y5),F(Y2),F(Y1)他們的joint pdf下手去做
另W1=F(Y10)-F(Y5) F(Y5)=W3-W1
|-1 0 1 0|
W2=F(Y2)-F(Y1) F(Y1)=W4-W2 | 0 -1 0 1|
|J|=|| 0 0 1 0||=1
W3=F(Y10) F(Y10)=W3 | 0 0 0 1|
W4=F(Y2) F(Y2)=W4
再來就作變數變換卡在範圍不知道怎麼定...
還是有別的作法可以做出來呢?
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