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PROBLEM # 4: Suppose we observe 3 sets of independent random variables: X1, X2, ... . Xn ~ N(Ox, 02); Y1, Y2, . .. , Yn ~ N(Oy, 02); and Z1, Z2, . .., Zn ~N(Ox + 0y, 02), which are also independent of each other. Let S2 = En(Xi-X)?/(n-1), $2 = EL,(Yi-Y)?/(n-1),and S? = Et-1(Zi -Z)2/(n-1), where X, Y and Z are respectively the sample means for the X's, Y's and Z's. Also we let S? = (1/3) (S2 + $2 + S?). 4.1 Use all observations to obtain the MLE of o