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

```

• Prev by Date: Inset BezierCurve
• Next by Date: creating a graphic in a text cell
• Previous by thread: Linear combinations of Expectation of EmpiricalDistribution
• Next by thread: Re: Linear combinations of Expectation of EmpiricalDistribution