Take a function of two random variables $Z = m(X,Y)$. If $X$ and $Y$ are independent, it should be possible to express the variance of $Z$ in terms of functional transforms of individual random variables, for instance like: $$ {\rm Var}(Z) = {\rm Var}(m(X,Y)) = m_0({\rm Var}(X),{\rm Var}(Y)) + {\rm Var}(m_1(X)) + {\rm Var}(m_2(Y)) $$ If so, what would be the functional of $m_0$, $m_1$ and $m_2$?
2026-03-26 21:09:25.1774559365
Total variance of a function of independent random variables
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