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Order statistics

  1. Feb 7, 2009 #1
    Three random variables are generated X1, X2, X3 on a spnning fair wheel three times. these variables are independent and uniformaly distributes on [0,1]. find probability that these values are none within +-d of each other where 0<=Y1<=Y2<=Y3<=1 is order statistics for randon variables.
    fY2Y3(y2,y3) = 2!fx(y) . fX(y) =

    what is fX(y)? can some one help?


    Pr[d<=Y2<=(1.2d), (y2+d)<=Y3<=(1-d)] =

    where y2 and y3 be placed in [0, 1]

    I can understand it but don't know how to do it....
  2. jcsd
  3. Feb 8, 2009 #2
    Hi Guys,

    Any help ????
  4. Feb 9, 2009 #3
    I'm interested in knowing how to do this, too. If the problem is asking what I think it is, it seems that it could be generalized to 2-dimensions. That might provide a simplified model of the number of clusters of balls remaining after the break shot in a game of pool (pocket billiards)....
  5. Mar 2, 2009 #4
    You don't need to the order statistics to solve this, however you will need to consider several separate cases where x1 or x2 fall within d of the endpoints or within 2d of each other. Also do the values fall on an interval or on a circle. The latter case will be a bit simpler to solve.
  6. Mar 3, 2009 #5
    thanks your solving problems
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