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Assume the integral is over the entire relevant space for X.

(1) E(X) = ∫ x dP

(2) E(X) = ∫ x dF(X)

If I asked you to calculate (1) or (2) for an arbitrary X, how does it look?

My only other understanding of E(X) is to do pdf times x, integrate, plug in bounds, but that's assuming X is nice enough to have such a pdf. I appreciate any replies!