Comment #6 on issue 3129 by [email protected]: Drastic change to sympy.stats: Adding concept of Probability Distributions on surface level
http://code.google.com/p/sympy/issues/detail?id=3129

Aaron, which notation would you prefer?

X = Binomial(2, 0.5, 'X') (what's currently offered)
X = RandomSymbol('X', Binomial(2, 0.5))
X = Binomial(2, 0.5).create_symbol('X')

I think a combination of the second and third ones would work. The second would be the general case, where you could pass in any function that works as a density function. The third would be the shorthand--in this case, we change the name of BinomialPSpace to Binomial, as with the other functions.

One thing I was wondering, Matthew, is there any use for the Symbol variable stored in PSpaces besides representation in the Density (which we've changed to use Lambda)? If not, we could probably get rid of it and simplify the hierarchy even more: Instead of
string >> sympy Symbol >> Random symbol, we'd have
string >> Random symbol

If I have time this week, I'll look over the code and try out these changes.

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