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/