Question

A certain raw material is classified as to moisture content X (in percent) and impurity Y (in percent). Let X and Y have the joint pmf given by
(a) Find the marginal pmfs, the means, and the variances.
(b) Find the covariance and the correlation coefficient of X and Y.
(c) If additional heating is needed with high moisture content and additional filtering with high impurity such that the additional cost is given by the function C = 2X + 10Y2 in dollars, find E(C).

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