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Problem 3. (20 points) If the joint distribution of X ~ N(ux, ox ) and Y ~ N(uy, o? ) is the bivariate normal distribution, then we say that (X, Y ) is a bivariate normal random variable with mean (Ux ) ER' and variance E = OX OXY OX , Y E R2x2, where ox,y is the covariance of X and Y. As a linear transformation of a normal random variable is also a normal random variable, a linear transformation of a bivariate normal random variable is also a bivariate normal random variable. Suppose ux = 4, My = -2, 08 = 1,ov = 4 and oxy = 1. Let W = 2X -Y. What is the joint distribution of (X,W)? That is, find the mean vector and variance matrix for (X, W)