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The following statement is true?

Suppose $E(Z\mid X)=0$. Then $E(Z\mid X,Y)=0$.

Any comments would be appreciated.

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    Generally this is not true, as you can see by taking $X$ to be an event distributed independent of $Z$. You should provide more context for the random variables $X,Y,Z$ unless you are asking an idle Question. – 2017-02-02

1 Answers 1

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Not nescessarily.

Suppose $X,Y\overset{iid}\sim\mathcal U\{-1,1\}$ and $Z=XY$

Then $\mathsf E(Z\mid X) = X~\mathsf E(Y) = 0$ but $\mathsf E(Z\mid X,Y)=XY\neq 0$ because $XY\in\{-1,1\}$ .