Re: How to generate random X given only min, max, mean?
- From: "John Uebersax" <jsuebersax@xxxxxxxxx>
- Date: 9 Jan 2006 01:53:09 -0800
> Suppose I know only -5 <= X <= 95 with Xmean = 75.
> I believe that means that P(-5 <= X <= 75) = 20% and
> P(75 <= X <= 95) = 80%, roughly. Right?
No.
Partly it depends on how you learned of the upper and lower limit. If
this is some theoretical or causal constraint, then 100% of the
distribution is between -5 and 95, inclusive.
But if these are given instead by random sampling -- i.e., someone
reports that in a sample, min = -5, max = 95, mean 75 -- wouldn't it
seem that somehow the sample size (N) would have to figure into
things?. That is, with, say, with a large N, wouldn't you be more
likely to get one or two extreme and unrepresentative high or low
values?
Hope this help.
--
John Uebersax
.
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