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Math Help - ordered uniform rand var

  1. #1
    Super Member Anonymous1's Avatar
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    ordered uniform rand var

    Let X_{(1)} \leq X_{(2)} \leq X_{(3)} \leq...\leq X_{(n)} be the ordered values of n independent uniform (0,1) random variables. Prove that for 1 \leq k \leq n+1,

    P(X_{(k)}-X_{(k-1)} > t) = (1 - t)^n

    Where X_{(0)} \equiv 0, X_{(n+1)} \equiv t.
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    Quote Originally Posted by Anonymous1 View Post
    Let X_{(1)} \leq X_{(2)} \leq X_{(3)} \leq...\leq X_{(n)} be the ordered values of n independent uniform (0,1) random variables. Prove that for 1 \leq k \leq n+1,

    P(X_{(k)}-X_{(k-1)} > t) = (1 - t)^n

    Where X_{(0)} \equiv 0, X_{(n+1)} \equiv t.
    You might start by calculating the joint pdf of X_{(k)} and X_{(k-1)}.
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