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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)
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  • 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



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