The infinite non-uniform discrete case is not much more difficult. If X is a finite or countably infinite set, f:X→R≥0 assigns a nonnegative value to each x∈X, and P is a probability distribution on Y, then Ex∼Pf(x)=∑x∈XP(x)f(x)
Very minor, but shouldn’t this read ”P is a probability distribution on X” not Y?
Very minor, but shouldn’t this read ”P is a probability distribution on X” not Y?