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MathGroup Archive 2006

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Re: Problem with using /.

  • To: mathgroup at smc.vnet.net
  • Subject: [mg69231] Re: Problem with using /.
  • From: Peter Pein <petsie at dordos.net>
  • Date: Sun, 3 Sep 2006 01:39:32 -0400 (EDT)
  • References: <edadil$pd0$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Nag schrieb:
> Hello:
> 
> I am trying to compute the moments of a distribution using the moment
> generating function, MGF[t,k]. Here is the relevant function for
> computing the j'th moment.
> 
> M[j_, t_, k_] :=    D[MGF[t, k], {t, j}] /. {u -> 0, Sum[Subscript[p,
> i],{i, 0, k}] = 1};
> 
> After taking the j'th derivative, need to set u to 0 and the sum of
> p(i)'s to 1.
> 
> When I execute M[3, u, 5], get the following error.(converted output to
> input form)
> 
> \!\(\*
>   StyleBox[
>     ErrorBox[\(Set::
>     "\<write\>" :
>       "\<Tag \!\(Sum\) in \!\(\(â??\+\(i = 0\)\%5\) p\_i\) is
>         Protected. \!\(\*ButtonBox[\"Moreâ?¦\",
> ButtonStyle->\"RefGuideLinkText\
> \", ButtonFrame->None, ButtonData:>\"General::write\"]\)\>"\)],
>     ShowStringCharacters->True]\)
> 
> Of course I can explicitly set p0+p1+..+p5 = 1 after executing M[3,u,5]
> but involves more effort as k increases.
> Is it possible to make the substitution work for general k in the
> function definition M[....]?
> 
> Best
> Nag
> 

Hi Nag,

you try to assign a value to Sum[...]; this becomes Set[Sum[...],0] -- 
but Sum is a Protected function. Furthermore, Set is not Rule.

I guess you wanted:

M[j_, t_, k_] := FullSimplify[D[MGF[t, k], {t, j}] /. u -> 0,
     Sum[Subscript[p, i], {i, 0, k}] == 1];

You can use Simplfy instead of FullSimplify too.

Peter


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