#9670: Bring probability/random_variable.py to 100% coverage
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Reporter: kcrisman | Owner: mvngu
Type: enhancement | Status: new
Priority: major | Milestone: sage-5.0
Component: documentation | Keywords:
Work_issues: | Upstream: N/A
Reviewer: | Author:
Merged: | Dependencies:
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Comment(by kohel):
Strictly speaking the probability space is a pair (X,p:X->RR),
and a random variable a function F:X->RR. Since there was no
suitable class of functions, the object returned by probability
space is essentially p, on which one can ask for the domain X
(as Python list, for lack of better datastructure of sets).
As such the printing function can be a bit confusing, since it
reports itself to be the probability space, but is implemented
as the function.
Now the probability function itself is a random variable (and
explicitly inherits from them), so expectation is well-defined,
as are other functions.
To do this properly, one needs to create or identify a class of
sets and their morphisms. Probability spaces would inherit from
sets and random variables and the probability function from their
morphisms.
In order to implement non-finite discrete random variables the
explicit sums should be replaced by closed forms, integrals or
similar computations.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/9670#comment:7>
Sage <http://www.sagemath.org>
Sage: Creating a Viable Open Source Alternative to Magma, Maple, Mathematica,
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