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MathGroup Archive 2001

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Re: a couple of gripes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg29759] Re: [mg29751] a couple of gripes
  • From: Andrzej Kozlowski <andrzej at tuins.ac.jp>
  • Date: Sun, 8 Jul 2001 01:00:05 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

on 01.7.7 3:25 PM, Joshua A. Solomon at J.A.Solomon at city.ac.uk wrote:

 > When I evaluate 
> Integrate[f[x]*If[x==y,1,0],{x,-Infinity,Infinity}]
> I don't get 
> f[y].

There is no reason why you should. However the following works:

In[9]:=
Integrate[f[x]*DiracDelta[x-y],{x,-Infinity,Infinity}]
Out[9]=
f[y]


> 
> When I evaluate 
> PDF[NormalDistribution[x,0],x]
> I don't get 
> 1.
> 

I am not a statistician, but this does not make any sense to me. What is
NormalDistribution[x,0] supposed to be ?  Are you, by any chance, not
confusing the PDF function (which is just the derivative of a CDF function)
with some sort discrete notion of "probability"?

Besides,  we have
In[29]:=
PDF[NormalDistribution[x,b],x]

Out[29]=
     1
------------
b Sqrt[2 Pi]

so even if we decided to define PDF[NormalDistribution[x,0],x] to be
something  it would be most un-natural to choose 1 rather than Infinity.

-- 
Andrzej Kozlowski
Toyama International University
JAPAN

http://platon.c.u-tokyo.ac.jp/andrzej/
http://sigma.tuins.ac.jp/~andrzej/



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