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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