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,