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/