5. Consider a bivariate distribution with joint pdf given by f(x, y) = cexp 0, X and Y are bivariate Gaussian random variables with joint PDF exp ( (2 3) /4 (x-3)(y-1)/3+ (y-1)2/4 fx, x (x, y) = C 87 5/9 Let W = 2X + Y and R = X + Y. Choose all the true statements. Keep in mind that the number of true statements is random; it's possible that all 10 statements are true . Note that (z) is the CDF of the Standard Normal Random Variable Z, and Q (z) is the Standard Normal Complementary CDF. P(2X + Y 6) = Q(2/V3). The correlation coefficient px y = 1/3. The correlation coefficient PW , R = 0.782. Y is Gaussian (1, 4). Var W] = 92/3. W and R are bivariate Gaussian random variables. Cov W, R = 20. The constant c = 5/9.6. (Computer problem) Using Theorem 5.21, write a Matlab function that produces a matrix of samples of a bivariate Gaussian distribution fx,y(x, y) with arbitrary values of #x, My, ox, oy, and px,y. Use this function to obtain 1000 samples of the following distributions. In each case, plot a 3-D mesh showing the value of fx.y(x, y) against (x, y). (a) ux = uy = 0, ox = oy = 1, and px.y = 0. (b) ux = HY = 0, ox = oy = 1, and px,y = 0.5. (c) ux = MY = 0, ox = oy = 1, and px y = -0.5.Let X = X1 X2 denote a bivariate normal (Gaussian ) ran- dom vector. Assume EX = 0 and EXXT Define Y1 = X1 + X2 and Y2 = -X1 + X2 1. Find the joint distribution of Y1 and Y2; find the marginal distributions of Y1 and Y2. 2. Find the conditional density of X1, given Y1; find the conditional den- sity of X1, given Y2. 3. Find the conditional mean and variance of X1, given Y1; find the conditional mean and variance of X1, given Y2