Quality-control checks on wood paneling involve counting the number of surface flaws on each panel. On a given 2 × 8 ft panel, let X be the number of surface flaws due to uneven application of the final coat of finishing material, and let Y be the number of surface flaws due to inclusions of foreign particles in the finish. The joint probability mass function p(x,y) of X and Y is presented in the following table. The marginal probability mass functions are presented as well, in the margins of the table. Find the covariance of X and Y
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y
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x
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0
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1
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2
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pX (x)
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0
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0.05
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0.10
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0.20
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0.35
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1
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0.05
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0.15
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0.05
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0.25
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2
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0.25
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0.10
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0.05
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0.40
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pY(y)
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0.35
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0.35
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0.30
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