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Consider two dice which each only have the numbers one, two and three on their faces,...

Consider two dice which each only have the numbers one, two and three on their faces, such that each number appears on two faces. One rolls these dice, and let X be the face value of the first dice, and Y be the face value of the second dice. We define W = X + Y and Z= X-Y.

1. Compute the joint probability mass function of W and Z.

2. Are W and Z independent?

3. Compute E[W] and E[Z].

Math   Statistics-And-Probability   
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