Let X, Xn have multivariate normal distribution MVN(u, o1n), where is nx 1 mean vector and...

  

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Let X, Xn have multivariate normal distribution MVN(u, o1n), where is nx 1 mean vector and I, is nxn identity matrix. Let Y = Z1GX, Y2 = E diXi, where cs and dis are constants. Show that Y and Y2 are indepen- dent iff 1Cd = 0. (Hint: Y and Y have bivariate normal distribution.) Let X, Xn have multivariate normal distribution MVN(u, o1n), where is nx 1 mean vector and I, is nxn identity matrix. Let Y = Z1GX, Y2 = E diXi, where cs and dis are constants. Show that Y and Y2 are indepen- dent iff 1Cd = 0. (Hint: Y and Y have bivariate normal distribution.)