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Math Help - independence

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    11

    independence

    I am having a problem with a dirichlet distribution

    For (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5)
    let Xk (k is a lower case) = [∑(from i=1 to k) Yi] / [∑(from i=1 to k+1) Yi] where k = 1,2,3

    How can I prove X = (X1, X2, X3) is independent?
    What I did was...

    (Y1, Y2, Y3, Y4) ~ D4(1,2,3,4;5) = (Z1, Z2, Z3, Z4) / (Z1+Z2+Z3+Z4+Z5) where Z ~ N(0,1), Z IID G(1/2)
    Now, we have
    X1 = Z1 / (Z1+Z2)
    X2 = (Z1+Z2) / (Z1+Z2+Z3)
    X3 = (Z1+Z2+Z3) / (Z1+Z2+Z3+Z4)

    I think if i can somehow show X1 and X2 are independent and X2 and X3 are independent then X1 and X3 are independent as well

    BUt i don't know how
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  2. #2
    Junior Member
    Joined
    Oct 2009
    Posts
    33
    i thought i got an answer for you but there was a mistake and I do not how to erase my thread so.... im sorry
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