Linear combinations of Expectation of EmpiricalDistribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg128132] Linear combinations of Expectation of EmpiricalDistribution*From*: Clemens Fruhwirth <clemens at endorphin.org>*Date*: Tue, 18 Sep 2012 03:40:19 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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

**Follow-Ups**:**Re: Linear combinations of Expectation of EmpiricalDistribution***From:*Bob Hanlon <hanlonr357@gmail.com>