# Independence, part 2

 A fair die is thrown two times independently. Let $$X$$ and $$Y$$ be the random variable indicating the outcomes of these two throws. Define $$Z = X + Y,$$ and define $$U$$ as the remainder when $$Z$$ is divided by $$6$$.

Which of the following statements are true?

1. $$X$$ and $$Z$$ are independent.
2. $$X$$ and $$U$$ are independent.
3. $$Z$$ and $$U$$ are independent.
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