Re: Linear combinations of Expectation of EmpiricalDistribution

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• Subject: [mg128171] Re: Linear combinations of Expectation of EmpiricalDistribution
• From: Clemens Fruhwirth <clemens at endorphin.org>
• Date: Thu, 20 Sep 2012 00:26:07 -0400 (EDT)
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```On 18 September 2012 00:33, Clemens Fruhwirth <clemens at endorphin.org> wrote:

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

For the archives:

Mathematica 8.0.4.0 has the following rule for
Statistics`ExpectationDump`iExpectation:

Statistics`ExpectationDump`iExpectation[Statistics`ExpectationDump`e_,
Statistics`ExpectationDump`f__] /;
Quiet[Internal`LiteralPresentQ[{Statistics`ExpectationDump`e,
FreeQ[{Statistics`ExpectationDump`e,
Statistics`ExpectationDump`f},
With[{Statistics`ExpectationDump`dom =
Statistics`ExpectationDump`g]},
FreeQ[Statistics`ExpectationDump`dom, Interval]]]] := \$Failed

To me, it reads as if it's a cut -- in the prolog sense of the word --
for the case where the domain of the DataDistribution is not an
interval. I am not sure what to make of that rule, as I don't see the
point of the cut for this special case. Maybe the second FreeQ is
supposed to be !FreeQ?

If I remove this rules from the rule set, all my examples work just fine..

{Expectation[x + y, dist],
Mean[TransformedDistribution[x + y, dist]],
Variance[TransformedDistribution[x + y, dist]]}
/. dist ->
{x \[Distributed] EmpiricalDistribution[{0, 1, 2}],
y \[Distributed] EmpiricalDistribution[{0, 10, 20}]}

{11, 11, 202/3}

I'll file a bug.
--
Fruhwirth Clemens http://clemens.endorphin.org

```

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