= Solution
{c}
For an outcome $\omega=(i,j)$, the two <random variables> are the coordinate maps
$$
\boxed{X(i,j)=i,\qquad Y(i,j)=j.}
$$
Their <marginal probability mass functions> are $p_X(i)=p_Y(j)=1/6$ on $\{1,\ldots,6\}$, and their <joint probability mass function> satisfies
$$
p_{X,Y}(i,j)=\frac1{36}=p_X(i)p_Y(j).
$$
Off that support, the same factorization holds with zeros. Hence \b[$X$ and $Y$ are <independent random variables>], by the <joint probability mass function> criterion for <independence>.
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