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Re: a couple of gripes
*To*: mathgroup at smc.vnet.net
*Subject*: [mg29765] Re: [mg29751] a couple of gripes
*From*: BobHanlon at aol.com
*Date*: Sun, 8 Jul 2001 01:00:09 -0400 (EDT)
*Sender*: owner-wri-mathgroup at wolfram.com
In a message dated 2001/7/7 2:37:22 AM, J.A.Solomon at city.ac.uk writes:
>When I evaluate
>Integrate[f[x]*If[x==y,1,0],{x,-Infinity,Infinity}]
>I don't get
>f[y].
>
>When I evaluate
>PDF[NormalDistribution[x,0],x]
>I don't get
>1.
>
$Version
"4.1 for Power Macintosh (November 2, 2000)"
If[x == y, 1, 0] is equivalent to DiracDelta[x - y]
Integrate[f[x]*DiracDelta[x-y], {x, -Infinity, Infinity}]
f[y]
Needs["Statistics`NormalDistribution`"];
The PDF of the normal distribution evaluated at the mean is
PDF[NormalDistribution[mu, sigma], mu]
1/(Sqrt[2*Pi]*sigma)
As the standard deviation, sigma, approaches zero, the PDF evaluated at the
mean
will become arbitrarily large, not 1. Presumably, you are trying to evaluate
the
CDF at the mean+ as the standard deviation approaches zero.
CDF[NormalDistribution[mu, 10^(-n)], mu+10^(1-n)]
(1/2)*(1 + Erf[5*Sqrt[2]])
%//N
1.
For arbitrarily large n this is the case with the standard deviation
arbitrarily small
and the CDF evaluated arbitrarily close to the mean.
Bob Hanlon
Chantilly, VA USA
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