4. (21 pts) Assume that the joint probability mass func- tion of the random variables X...

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4. (21 pts) Assume that the joint probability mass func- tion of the random variables X and Y is given like in the table right. Find the marginal probability mass func- tions of X and of Y. Are X and Y independent? Why? Show your work in detail! X 0 1 2 0 0.10 0.17 0.06 y 1 0.11 0.23 0.14 2 0.05 0.08 0.06 4. (21 pts) Assume that the joint probability mass func- tion of the random variables X and Y is given like in the table right. Find the marginal probability mass func- tions of X and of Y. Are X and Y independent? Why? Show your work in detail! X 0 1 2 0 0.10 0.17 0.06 y 1 0.11 0.23 0.14 2 0.05 0.08 0.06