Consider 3 random variables $X$, $Y$, $Z$. Suppose:
- $E(X)=0$
- $E(X|Y) =0$
- $Z\perp Y $
Does this imply $E(X|Y,Z) = E(X|Z)$?
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Sign up to join this communityConsider 3 random variables $X$, $Y$, $Z$. Suppose:
Does this imply $E(X|Y,Z) = E(X|Z)$?
If you have
X Y Z prob
0 0 0 1/4
0 0 1 1/4
+1 1 0 1/4
-1 1 1 1/4
then the conditions are satisfied
while $E[X \mid Y=0, Z=0] = 0$ while $E[X \mid Z=0]=\frac12$