Show that $E(X)$ = $E[(X|Y=y1) * 1(Y=y1)+ (X|Y=y2) * 1(Y=y2)]$
where $Y$ can be either $y1$ or $y2$ with some probabilities.
I suppose the result will not be restricted to $Y$ being binary, and the proof should extend.
Show that $E(X)$ = $E[(X|Y=y1) * 1(Y=y1)+ (X|Y=y2) * 1(Y=y2)]$ for RV's $X$ and $Y$
Arshdeep
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