Re: Mathematica Integration help

*To*: mathgroup at smc.vnet.net*Subject*: [mg86138] Re: Mathematica Integration help*From*: Jens-Peer Kuska <kuska at informatik.uni-leipzig.de>*Date*: Mon, 3 Mar 2008 04:40:08 -0500 (EST)*References*: <fqetdm$jjs$1@smc.vnet.net>

Hi, look what happens when you compute from: res = Integrate[ Product[1/(E^((Subscript[x, i] - \[Mu])^2/(2*\[Sigma]^2))* Sqrt[2*Pi*\[Sigma]^2]), {i, 1, n}], \[Mu]] D[res,\[Mu]] and see that the result is *not* Product[1/(E^((Subscript[x, i] - \[Mu])^2/(2*\[Sigma]^2))* Sqrt[2*Pi*\[Sigma]^2]), {i, 1, n}] this obvious a bug. Regards Jens Francogrex wrote: > Hi I'm new to Mathematica, I don't know if there are other help forums > beside this one. I need help estimating the integrated likelihood > function with mathematica 6. > > My function is below(all equations below are in mathematica raw input > form, pls convert to standard form to see how they really look like): > > Integrate[Product[1/(E^((Subscript[x, i] - \[Mu])^2/(2*\[Sigma]^2))* > Sqrt[2*Pi*\[Sigma]^2]), {i, 1, n}], \[Mu]] > > > The result that it's giving me is the following: > > -(2^(-(1/2) - n/2)* > E^((n*(-\[Mu] + Subscript[x, i])^2)/(2*\[Sigma]^2))* > Pi^(1/2 - n/2)*\[Sigma]* > (Sqrt[\[Sigma]^2]/(E^((-\[Mu] + > Subscript[x, i])^2/(2*\[Sigma]^2))*\[Sigma]^2))^n* > Erf[(Sqrt[n]*(-\[Mu] + Subscript[x, i]))/(Sqrt[2]*\[Sigma])])/ > Sqrt[n] > > > But I know from a publication I've read that the result doesn't > involve the Erf, but it's the following: > > 1/(E^(Sum[(Subscript[x, i] - OverBar[x])^2, {i, 1, > n}]/(2*\[Sigma]^2))* > (Sqrt[n]*(2*Pi*\[Sigma]^2)^((n - 1)/2))) > > where: OverBar[x] = Sum[Subscript[x, i], {i, 1, n}]/n > > Is there any way to get Mathematica to output that? Thanks >