Sum.doit() gives incorrect results with Random Indexed Variables

[Smit-create]

While working on #19428, I came across the following error

>>> from sympy.stats import *
>>> from sympy import symbols, S, Eq, Sum
>>> B = BernoulliProcess('B', S(1)/2, 1, -1)
>>> t = symbols('t', positive=True, integer=True)
>>> expr = Sum(B[t], (t,0,5))
>>> expr
Sum(B[t], (t, 0, 5))
>>> expr.doit()  # this should not consider B[t] equal in all the cases as it is random variable
6*B[t]          # incorrect result

Expected behaviour, it should produce: B[0] + B[1] + B[2] + B[3] + B[4] + B[5]

[czgdp1807]

That's quite a problem. Can you please make a PR to fix it?
Does the problem exist with parent class of RandomIndexedSymbol?

[Smit-create]

Does the problem exist with parent class of RandomIndexedSymbol?

I need to look into it

[Smit-create]

Does the problem exist with parent class of RandomIndexedSymbol?

The problem I see here is:

>>> B = BernoulliProcess('B',0.2)
>>> B[t]
B[t]
>>> B[t].free_symbols
{B[t]}

Free symbols is returning B[t], but I think for RandomIndexedSymbol, we should return {B[t], t} if t is symbolic else {B[t]} when t is not symbolic??