Let a random variable $X$ be given with $P_X$ supported over $\mathcal{X}$. What are the necessary conditions for the existence of a boolean function $f:\mathcal{X}\to \{0,1\}$ such that $\mathsf{var}(f(X))=\mathsf{var}(X)$?
$\begingroup$
$\endgroup$
4
-
1$\begingroup$ $\textrm{Var}(X)\le 1/4$ is a necessary condition. $\endgroup$– Christian RemlingCommented Dec 1, 2015 at 7:32
-
$\begingroup$ Can you please elaborate on that? Any proof? or at least any reference? $\endgroup$– math-StudentCommented Dec 1, 2015 at 14:23
-
$\begingroup$ $f(X)$ only takes the values $0,1$. $\endgroup$– Christian RemlingCommented Dec 1, 2015 at 17:42
-
$\begingroup$ $f(X)$ makes no sense to me. $\endgroup$– Ramiro de la VegaCommented Dec 2, 2015 at 13:23
Add a comment
|