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Linear combinations of Expectation of EmpiricalDistribution


Dear MathGroup,

The expectation for any linear combination of random values is the
linear combination of the respective expectations of the random
values, such as

E(aX+bY) = aE(X) + bE(Y)

I wonder why Mathematica can't resolve this rule when
EmpiricalDistributions come into play. For instance,

Expectation[
 x + y, {x \[Distributed] EmpiricalDistribution[{0, 1, 2}],
  y \[Distributed] EmpiricalDistribution[{0, 10, 20}]}]

I came up with:

ExpectationX[
  a_ + b_, {x_ \[Distributed] xdist_, y_ \[Distributed] ydist_}] :=
 a + b //. {x -> Expectation[x, x \[Distributed] xdist],
   y -> Expectation[y, y \[Distributed] ydist]}

to resolve at least simple addition. But before I put more work into that:

* Am I missing an assumption here or some syntax? Or is this rule just
not built into Mathematica?

* Is that in general the right approach to extend Mathematica?

Thanks!
-- 
Fruhwirth Clemens http://clemens.endorphin.org



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