Re: Linear combinations of Expectation of EmpiricalDistribution

*To*: mathgroup at smc.vnet.net*Subject*: [mg128145] Re: Linear combinations of Expectation of EmpiricalDistribution*From*: Clemens Fruhwirth <clemens at endorphin.org>*Date*: Wed, 19 Sep 2012 04:55:18 -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*References*: <20120918074019.14F1B6847@smc.vnet.net> <CAEtRDSd3DFdjW9UayPVrrCLLvoNbXUeEUdUz+5kB1sKzyaxNAg@mail.gmail.com>

On 18 September 2012 16:13, Bob Hanlon <hanlonr357 at gmail.com> wrote: > Expectation[x + y, > {x, y} \[Distributed] EmpiricalDistribution[ > Thread[{{0, 1, 2}, {0, 10, 20}}]]] > > 11 This creates a single multivariate distribution that does not represent two independent random variables[*]. Ideally, Expectation would not only know about the universally applicable linear combination law, but also rules for the independent random variable case, such as E(A*B) = E(A)*E(B). There are other laws as well that apply to other Moment-s that I would like to see working for EmpiricalDistribution. Only EmpiricalDistribution seems to be affected. Specifying two independent NormalDistribution-s just works fine: Expectation[ x + y, {x \[Distributed] NormalDistribution[3, a], y \[Distributed] NormalDistribution[10, b]}] 13 [*] That could be fixed by simulating independence /. Thread -> Tuples -- Fruhwirth Clemens http://clemens.endorphin.org

**References**:**Linear combinations of Expectation of EmpiricalDistribution***From:*Clemens Fruhwirth <clemens@endorphin.org>