T Z Please answer the question If to and y are bivariate normal, then not only every Linear combination axt by has the normal distribution , but also every two linear combinations, dixt bit and dirt bay, have again a bivarlate normal distribution ( ", b, a1 , br , a2 , by are all constants ) Take the above statement as a groen fact . let X and y be bivariate normal, with means Jux =My z( and variances 0% = Gy 21, and correlation px, y= 0.5. Define Z. = xty and 22 = X42Y ") Find the mean M Z. = E ( ZI ) ; M 2 2 = E ( Zz ), and the variance 02 = var ( Z. ) , 62, = Var( 2 2). b ) Compute ECZ, 1Z, = 0) and Var ( 22 12120 )