Exercise 1 A certain raw material is classified by its moisture content X (in percent) and impurity Y (in percent). Let X and Y have the joint pmff (x, y) given by X 1 2 3 1 0.05 0.05 0.25 Y 2 0.10 0.20 0.35 (a) Find the marginal pmf's for X and Y, their means, and their variances. You may give the marginal pmf's by either writing them each as a piecewise function or as a table. (b) Find the covariance and the correlation coefficient of X and Y