Let X & Y be two independent random variables. I was wondering if someone could clarify the manipulation of this conditional expectation.
- if E(XY|X) = E(X(Y|X))
- if E(XY|X) = XE(Y|X)
Are either of these correct?
2026-04-02 09:30:51.1775122251
help with manipulation of conditional expectation
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The second one is correct. The first one does not make sense as it is. You probably meant $E(XY|X)=E(XE(Y|X))$. This is false. LHS is $XEY$ and RHS is $(EX)(EY)$