Compare a signed dice difference with its absolute value

A fair die is thrown once and $X$ is its score. Calculate $E(X)$ and show that $\operatorname{Var}(X)=35/12$. The die is thrown twice, with scores $X_1,X_2$. Tabulate the distribution of $Y=\lvert X_1-X_2\rvert$ and find $E(Y)$. Let $Z=X_1-X_2$. State with reasons, without necessarily evaluating the quantities, whether (a) $E(Z^2)=E(Y^2)$ and (b) $\operatorname{Var}(Z)=\operatorname{Var}(Y)$.