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From: CHARLES GILLINGHAM <cgillingham1@me.com>
Newsgroups: comp.soft-sys.math.mathematica
Subject: Re: Bug with ProbabilityDistribution
Date: Fri, 11 Apr 2014 06:08:34 +0000 (UTC)
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On Apr 10, 2014, at 12:06 AM, Bill Rowe <readnews@sbcglobal.net> wrote:

> On 4/9/14 at 4:14 AM, cgillingham1@me.com (CHARLES GILLINGHAM) wrote:
>
>> Evaluate this:
>
>> ProbabilityDistribution[
>> Piecewise[{{0, x1 == 1 && x2 == 1}, {1/2, x1 == 1 && x2 == 0}, {0,
>> x1 == 0 && x2 == 1}, {1/2, x1 == 0 && x2 == 0}}], {x1, 0, 1,
>> 1}, {x2, 0, 1, 1}
>> ]
>
> Start with a fresh session and pay attention to the syntax
> coloring. Note that x1 and x2 are undefined and your syntax does
> not make these local variables. That is entering
>
> f[x_]:=2 x
>
> will cause x to be colored differently than your x1, x2 above.
>
> You get undefined as a result since x1 and x2 are never defined.

This is an interesting issue (that may point to other problems), but it doesn't explain the particular bug I am looking at. The variables are also undefined in Bob Hanlon's workaround. Try this, which is exactly equivalent, and works fine:

ProbabilityDistribution[
 Piecewise[{{0, (x1 != 0 && x1 != 1) || x2 != 0}}, 1/2] , {x1, 0, 1, 1}, {x2,
  0, 1, 1}]
PDF[%][{1,1}]