Question: Suppose X is a random variable taking the values 1, 2, or 3, each with equal probability (as if rolling a fair 3-sided die). Suppose

Suppose X is a random variable taking the values 1, 2, or 3, each with equal probability (as if rolling a fair 3-sided die). Suppose Y is independently drawn from the same distribution. What is the variance of the absolute difference between X and Y , i.e., what is var( |X Y | )?

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