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: У х 0.15 0.12 0.11 0.10 0.09 0.07 0.05 0.04 2 0.06 0.05 0.04 0.02 0.02 3 0.04 0.03 0.01 Find the conditional probability mass function pyx♥ | 1) Find the conditional probability mass function Pyxv | 2) a. b. Find the conditional expectation E(Y|X = 1). C. Find the conditional expectation E(X | Y = 2). d.

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