From: Daniel Carrera <dcarrera@...>
Date: 2003-04-20T09:53:01+09:00
Subject: Re: Biased weighted random?

On Sat, Apr 19, 2003 at 07:32:36AM +0900, Chris Pine wrote:
> But it didn't.
> 
> Look at Hal's example, with the weights of 2, 4, 6, and 8.  The object with
> weight 2 came up *more* than half as much as the object with weight 4.  The
> ratios (the probabilities) were changed.

If you keep the ratios constant, the probabilities *must* change.  Take 
for example:

event 1 has prob .4
event 2 has prob .3
event 3 has prob .3

If on the first trial I select event 1, and I don't want repetitions, then 
the new probability of event 1 is 0.  If we keep the ratio between the 
probabilities of events 2 and 3 constant, then necessarily the new 
probabilities are:

event 1 has prob 0
event 2 has prob .5
event 3 has prob .5

So yes, the definitelly have to change.

As for Hal's experiment, the sample was too small to be statistically 
significant (it was small enough to fit in a couple of lines).  You will 
almost never see that kind of "perfect" distribution.  That kind of 
distribution is not representative of what a typical random distribution.

-- 
Daniel Carrera
Graduate Teaching Assistant.  Math Dept.
University of Maryland.  (301) 405-5137