Does the law of total expectation hold for more than one conditioning variables, i.e. $E[E[X|Y, Z]]= E[X]?$ It is easy to show it for discrete Y, Z, but does it hold for continuous conditioning sets as well?
2026-03-28 03:26:24.1774668384
Law of total expectation for larger conditioning sets.
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It holds for any number of variables. More generally, $E(E(X|\mathcal G))=EX$ for any sigma algebra $\mathcal G$.