A fair die is rolled. If the result is greater than 4, a fair coin is...

A fair die is rolled. If the result is greater than 4, a fair coin is flipped, and otherwise, an unfair coin with P[H] = 2/3 is flipped. The outcome of the die roll is mapped to X, and the outcome of the coin flip is mapped to Y , with 1 for heads and −1 for tails.

(a) Find the joint PMF.

(b) Find both marginal PMFs. Do the marginal PMFs indicate independence?

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