Solving Order Statistics with Three Uniformly Distributed Random Variables

[robert5]

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?

Also,

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...

 

[robert5]

Hi Guys,

Any help ?

 

[Adeimantus]

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)...

 

[bpet]

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.

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.

 

[gurkan]

thanks your solving problems