Can $g(X) = \mathbb{E}[X | X>k] - E[X]$ be simplified as a single expectation as $[E | q(X)]$?
2026-03-27 01:42:20.1774575740
Calculate Difference between Expectation and Conditional Expectation
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It is not totally clear to me what you are asking for but if
$$q(X)=\left(\dfrac{\mathbb I[X>k]}{\mathbb P (X>k)} -1 \right)X$$ where $\mathbb I[A]$ is an indicator function for an event and $\mathbb P (A)$ is the probability it is $1$,
then $g(X) = \mathbb E[q(X)]$