Let $X$ be an arbitrary random variable. Given an equation l.h.s. = r.h.s. does this imply $E[l.h.s.| X=x] = E[r.h.s.|X=x]$?
Cheers.
2026-03-28 16:21:28.1774714888
Is it correct to take the conditional expectation on both sides?
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Yes, if the equation means that the two sides are always equal to each other. It's the same as saying: if two functions are identically equal, then their integrals are equal.