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.