. Consider two jars, Jar M and Jar W. In Jar M, there are 3 balls numbered 0, 1, 2. In Jar W there are 3 balls numbered 1, 2, 3. A ball is drawn from Jar M, then a. ball is drawn from J or W. Dene M as the number on the ball from Jar M and W the number on the ball drawn from Jar W. Let X =WM and Y = min{I/V, M2}(Minimurn of W and M2). (a) Find the joint probability mass function of X and Y. (b) Are X and Y independent? Use the denition of independence to support your answer. (c) Compute the Oomph/f, 2\") (ie, Correlation coefcient of x/Jf and 2"). (d) Compute the Cov(22+Y, 4%)?) and Corr(22+y,4\\/) . (e) Find the probability mass function of X given Y = 1 (ie, 33(me = 1))