Question: A box contains three coconut candies, five hazelnut chocolates, and two peanut butter chocolates. A sample of four sweets is chosen from the box. Let

A box contains three coconut candies, five hazelnut chocolates, and two peanut butter chocolates. A sample of four sweets is chosen from the box. Let X, Y, and Z be the number of coconut candies, hazelnut chocolates, and peanut butter chocolates in the sample, respectively. (i) Find the joint distribution of (X, Y ). (ii) Find the marginal distributions of X, Y, and Z. (iii) Are X and Y independent? Are X and Z independent?

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