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Math Help - question about cdf distribution

  1. #1
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    Angry question about cdf distribution



    (x(i) in the beginning, if you cant read it)
    How would I start on this, i'm not too sure.
    Last edited by Sneaky; October 21st 2010 at 12:18 PM.
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  2. #2
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    Fx(n)(x) = Px(n)(X(n)<=x)
    Fx(n)(x) = Px1...xn(max{x1,...xn}<=x)
    Fx(n)(x) = Px1...xn(x1<=x,...,xn<=x)
    Fx(n)(x) = Px1(x1<=x)*...*Pxn(xn<=x)
    Fx(n)(x) = Fx1(x)*...*Fxn(x)
    Fx(n)(x) = Fx1(x)*...*Fxi(x)*...*Fxn(x)
    Fx(n)(x) = Fx1(x)*...*Fx(n-1)(x)*Fxi(x)
    Fxi(x) = Fx(n)(x) / Fx1(x)*...*Fx(n-1)(x)

    not sure where to go from here...
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  3. #3
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    Quote Originally Posted by Sneaky View Post


    (x(i) in the beginning, if you cant read it)
    How would I start on this, i'm not too sure.
    example of what X(n) means

    X1=0.5 X(1) = 0.1 (so it is increasing...)
    X2=0.7 X(2) = 0.2
    x3=0.96 X(3) = 0.45
    x4=0.45 X(4) = 0.5
    x5=0.2 X(5) = 0.7
    x6=0.1 X(6) = 0.96

    Fx(n)(X) = Px(n)(Xn<=X)

    so a cumulative distribution function
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  4. #4
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    Quote Originally Posted by Sneaky View Post


    (x(i) in the beginning, if you cant read it)
    How would I start on this, i'm not too sure.
    It looks like you want the cdf of the ith order statistic for a discrete random variable. I suggest you do some research in that direction.
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