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MathGroup Archive 2001

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Re: a couple of gripes

  • To: mathgroup at smc.vnet.net
  • Subject: [mg29766] Re: a couple of gripes
  • From: bob_jones96 at hotmail.com (Bob Jones)
  • Date: Sun, 8 Jul 2001 01:00:10 -0400 (EDT)
  • References: <9i6aan$okh$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

"Joshua A. Solomon" <J.A.Solomon at city.ac.uk> wrote in 
<9i6aan$okh$1 at smc.vnet.net>:

> 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.
> 
> js

Dear Joshua,

Do you really expect it to to do either one of these things?

Have you ever heard of the Dirac delta function?  I think it is really what 
you wanted to use in gripe one.

Integrate[f[x] DiracDelta[x - y], {x, -Infinity, Infinity}] gives f[y]

Why would a normal distribution with zero standard deviation evaluate to 1 
at the mean?  This is actually one way to construct the Dirac delta 
function.

Limit[PDF[NormalDistribution[x, y], x], y -> 0] gives Infinity not 1.

(Don't forget to load Statistics`ContinuousDistributions` if you need to.)

Maybe I just don't understand what you are trying to do.  If not, please 
forgive my unsolicited advice.

Cheers,


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