Following this answer, it is claimed that we can solve the problem in the following way:
∫∞c(x−c)dF(x)=limy→∞(y−c)F(y)−∫∞cF(x)dx.
where F is the cumulative distribution function of a given random variable.
Does this limit exist though? In my understanding, since distribution function saturates at 1, the first limit should converge to infinity? What am I missing?
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