I think its a pretty good idea. I'm not a sympy dev, but I stumbled on this 
thread because I was looking for some way to do this.

On Tuesday, December 15, 2015 at 1:05:20 PM UTC-5, Francesco Bonazzi wrote:
>
> I started recently some work on a symbolic expression for variance and 
> covariance in *sympy.stats* module:
>
> https://github.com/sympy/sympy/pull/10247
>
> The current *stats* module defines functions such as *P (probability), E 
> (expectation), variance, covariance, moment, *and so on, to perform the 
> integral given random variables or conditions on random variables.
>
> I think it's convenient to also have the possibility to operate at a 
> higher level of abstraction, by keeping unevaluated symbolic expressions 
> and operating with their properties on them.
>
> The idea is to define a class with the same name of the function, with 
> capital first letter:
>
>    - Expectation( ) vs expectation( )
>    - Probability( ) vs probability( )
>    - Variance( ) vs variance( )
>    - ... and so on ...
>    
> The latter ones are the existing functions, whereas the first ones are 
> classes that create the unevaluated expression.
>
>
> The method *.doit()* calls the corresponding function to perform the 
> integral.
>
>
> A similar relationship already exists in SymPy:
>
>    - Integral( ) vs integrate( )
>    - Derivative( ) vs diff( )
>    - Sum( ) vs sum( )
>
> *.doit()* calls the function.
>
>
> I'd like to have some feedback before going on. Do you think this is a 
> good idea? Would you merge this once it's finished?
>

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