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change of variable newbie question

  • To: mathgroup at smc.vnet.net
  • Subject: [mg115077] change of variable newbie question
  • From: Lynn Bu <bu.lynn5 at gmail.com>
  • Date: Thu, 30 Dec 2010 04:12:06 -0500 (EST)

Hi,

I work in Mathematica 7.0 and would like to know how to code according to
the integral:

 S[t] = Integral[p[x,t]Log[p[x,t]]dx, {-infinity, infinity}]

Where:

 p[x,t] = (1/t=CE=B4)F(x/ t=CE=B4)



There is a change of the variable x into:



y =  x/ t=CE=B4

In which case; the integral comes out to a form looking like:



S(=CF=84) = A + =CE=B4=CF=84



where:

A =E2=89=A1 Integral[dy F(y) Ln[F(y)], {-infinity, infinity}]

And



=CF=84 =E2=89=A1 Ln(t)



Would appreciate the assistance =E2=80=93 I tied a number of ways, Solve, combining
first two equations, etc. Note first equation is Shannon entropy form.

Thanks if you can help,

L.B.


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