"Cristian-Augustin Saita" <[EMAIL PROTECTED]> wrote in
message as86v0$9kh$[EMAIL PROTECTED]">news:as86v0$9kh$[EMAIL PROTECTED]...
> I'm interested in the probability that two intervals selected "at
> random" from among those that satisfy the constraints will
intersect.
>
> "At random" here means that the intervals satisfying the constraints
> follow an uniform distribution.
>
>
Well maybe, but what do you think this should mean? The following four
ways of specifying an interval (A,B) yield different answers:
(1) choose B uniformly on (0,1), then A uniformly on (0,A).
(2) choose A uniformly on (0,1), then B uniformly on (A,1).
(3) choose (X,Y) independent and uniform on (0,1), then set
A=min(X,Y), B=max(X,Y).
(4) choose the length L to be uniform on (0,1), then choose A to be
uniform on (0,1-L), and set B=A+L.
David Jones
.
.
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