I'd like to find the expected value of a discrete random variable without specifying a particular distribution so I can still manipulate the entire expression symbolically.
For example, how would I get the rhs of the following expectation using summation in sympy?
If n is unknown, you can use summation
In [45]: i, n = symbols('i n', integer=True)
In [46]: p, a = symbols('p a', cls=Function)
In [47]: summation(p(a(i))*a(i), (i, 0, n))
Out[47]:
n
___
╲
╲ a(i)⋅p(a(i))
╱
╱
‾‾‾
i = 0
If n is known, you'll probably want to just represent the actual sum:
In [48]: n = 10
In [49]: sum(p(a(i))*a(i) for i in range(1, n+1))
Out[49]: a(1)⋅p(a(1)) + a(2)⋅p(a(2)) + a(3)⋅p(a(3)) + a(4)⋅p(a(4)) + a(5)⋅p(a(5)) + a(6)⋅p(a(6)) + a(7)⋅p(a(7)) + a(8)⋅p(a(8)) + a(9)⋅p(a(9)) + a(10)⋅p(a(10))