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Re: DiscreteUniformDistribution PDF isn't piecewise?

• To: mathgroup at smc.vnet.net
• Subject: [mg107703] Re: DiscreteUniformDistribution PDF isn't piecewise?
• From: "richard.wesley.todd" <richard.wesley.todd at gmail.com>
• Date: Wed, 24 Feb 2010 06:17:57 -0500 (EST)
• References: <hlqu3v$go8$1@smc.vnet.net> <201002220807.DAA28826@smc.vnet.net>

Below is the response I got back from WRI.

 **********

Hello,

Thank you for the email.

Question 1: PDF[DiscreteUniformDistribution[{1, 6}]] returns one pure
function, not one piecewise function.

Answer: In released versions, the domain of the distribution is not
explicitly included in PDF. This will change in a future release. The
CDF
is defined over the whole real line and is defined as a Piecewise
function
in released versions.

Question 2:
dist = DiscreteUniformDistribution[{1,6}];
In[40]:= PDF[dist, #] & /@ Range[-10,10]
Out[40]= {0,0,0,0,0,0,0,0,0,0,0,1/6,1/6,1/6,1/6,1/6,1/6,0,0,0,0}
In[41]:= PDF[dist, #] & /@ N[Range[-10,10]]
Out[41]= {0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0}

Answer: about 0 probability when the point is not explicitly an
integer is
still a point of discussion here. Viewed strictly as a distribution on
integers, the result would be correct because N[integer] is not an
integer.
Viewing the point as being equal to an integer would argue that the
probability should be non-zero.

• References:
  • Re: DiscreteUniformDistribution PDF isn't piecewise?
    • From: "Nasser M. Abbasi" <nma@12000.org>