Why does it hold: $ \operatorname{Var}(\mathbb{E}[X\mid\theta]\mid P) = \operatorname{Var}(X\mid P) - \operatorname{Var}(X\mid\theta)$, where $\theta$ are normal random variables? It looks a bit like projection theorem, but I can't apply it here.
2026-03-27 10:47:48.1774608468
Conditional variance: $ \operatorname{Var}(\mathbb{E}[X\mid\theta]\mid P) = \operatorname{Var}(X\mid P) - \operatorname{Var}(X\mid \theta)$
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