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From: sarwate@uicsl.UUCP
Newsgroups: sci.math
Subject: Re: Need formula for Normal Distributio
Message-ID: <71100001@uicsl>
Date: Wed, 5-Nov-86 10:34:00 EST
Article-I.D.: uicsl.71100001
Posted: Wed Nov  5 10:34:00 1986
Date-Received: Sun, 16-Nov-86 06:35:43 EST
References: <146@helm.UUCP>
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Nf-ID: #R:helm.UUCP:146:uicsl:71100001:000:1421
Nf-From: uicsl.UUCP!sarwate    Nov  5 09:34:00 1986


The problem posed is to find a function F(X,S,A) so that when X1, X2, . . . Xn
are n (successive?) outputs of the BASIC random number generator, the numbers
Y1=F(X1,S,A), Y2=F(X2,S,A), etc form a sample with mean A and standard deviation
S. It is also desired that the Y's be in the range 0-100 (A is in that range,
as is S), and there is also a reference to a normal (Gaussian?) distribution.

Two solutions to this problem have been proposed. However, neither fully solves
the original problem. In fact, the original problem may not have a solution at
all. It is difficult to tell because the problem itself is not properly posed,
and it is not clear what exactly the author of the problem wants.

If the Y's are indeed meant to represent samples from a Gaussian distribution,
then one cannot guarantee that they will be in the range 0-100. Of course, in
practice, if S is small enough, the Y's will (with very high probability)
satisfy this restriction.  On the other hand, is S=9 considered small in
comparison with A=90 ? And if so, how can one guarantee that the sample values
are in the range 0-100 ?

It is not clear how either of the methods proposed by Kenny and Schaffer will
give a sample with average EXACTLY A (if indeed this is what is desired). Given
a large enough sample, the average value will be APPROXIMATELY A and the
standard deviation will be APPROXIMATELY S, but that is all that one can expect.