In a piston assembly, the specifications for the clearance between piston rings and the cylinder wall are very tight. In a lot of assemblies, let X be the number with too little clearance and let Y be the number with too much clearance. The joint probability mass function of X and Y is given in the table below: y 2 3 х 0.15 0.12 0.11 0.10 0.09 0.07 0.05 0.04 0.05 2 0.06 0.04 0.02 0.03 3 0.04 0.02 0.01 Find the marginal probability mass function of X. Find the marginal probability mass function of Y. Are X and Y independent? Explain. Find µx a. b. c. d. and Hy. Find Ox and Oy. e. Find Cov(X, Y). Find p(X, Y). f. g.

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