Comment #3 on issue 3129 by nathan.f...@gmail.com: Drastic change to sympy.stats: Adding concept of Probability Distributions on surface level
http://code.google.com/p/sympy/issues/detail?id=3129

It looks like one of the things you're proposing to replace PSpace with Probability Distribution and clean it up so that it is user-visible. I'm generally happy with this. There is a lot we can do to clean up the internals of sympy.stats and this might be one of them. It would be great to have a second developer go over the code in depth and provide a second perspective.


But, formally probability distributions and spaces are different things. Might cause confusion if we say something is a p-distribution when it has the capabilities of a p-space? I don't have any experience in formal probability theory and I don't know if you're even thinking about these as you were implementing stats...:
http://en.wikipedia.org/wiki/Probability_distribution
http://en.wikipedia.org/wiki/Probability_space


I'm much more hesitant to affect the interface however. I think that single-line random variable creation is important. It allows introductory users to jump into sympy.stats much more quickly. I like auto-generation of symbols if not provided (this makes the code look more like math) but I'm not going to fight very hard for it.

More like math, but less consistent with sympy.
i.e., to make a regular symbol you do
x = Symbol('x')

The only other example of a *specific* symbol I can find is MatrixSymbol, which also has the same notation (symbol name first, arguments [in this case dimensions] second):
A = MatrixSymbol('A', 3, 4) # 3x4 matrix

I just reason that making random symbols should be the same:
X = RandomSymbol('X', <stuff>)

Of course, we could go the other way and add auto-generation for regular symbols :)
x = Symbol()
x
x1


- Unambiguous creation of new random variables
* Can you expand upon this?

Basically, you can call:
X = Binomial(1, 2)
Y = Binomial(1, 2)

And you would get different "results", different objects, while the notation makes it look like you're storing a static result "Binomial(1, 2)" to both X and Y. I think


Waiting to expose the internals later sounds like a good idea. Right now the important thing is to figure out the right notation. I wonder what Aaron thinks about this?

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