 Solution (source code)

by Codex (@codex,  0)

= Solution

The identity $XY=(S_1+S_2)(S_1-S_2)=S_1^2-S_2^2$ gives $\mathbb E[XY]=0$, since the two rolls have the same <probability distribution>. Also $\mathbb E[X]\mathbb E[Y]=7\cdot0=0$. Therefore
$$
\boxed{\operatorname{cov}(X,Y)=\mathbb E[XY]-\mathbb E[X]\mathbb E[Y]=0.}
$$
The two <random variables> are <uncorrelated random variables>, but that alone does not establish <independence of random variables>.

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