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,