## Two cool things about dice!

Just discover two cool things about dice, Suppose we have two (fair) 6-sided dice, let $$Y$$ be the reminder of the product of the two numbers divided by 7, i.e., $$Y = X1 \times X2 (\text{ mod } 7)$$, guess what the distribution of $$Y$$ is? Uniform 1,..., 6

If it …