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6. (10 points) Let (X1,Y1),�,(Xn,Yn) be a sample from a N(1,2,12,22,).pdf

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6. (10 points) Let (X1,Y1),,(Xn,Yn) be a sample from a N(1,2,12,22,) population. Show that the MLEs of 12,22, and when 1 and 2 are assumed to be known are ~12=(1/n)i=1n(Xi1)2,~22=(1/n)i=1n(Yi2)2, and ~=[i=1n(Xi1)(Yi2)/n~1~2] respectively, provided that n3..

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6. (10 points) Let (X1,Y1),,(Xn,Yn) be a sample from a N(1,2,12,22,) population. Show that the MLEs of 12,22, and when 1 and 2 are assumed to be known are ~12=(1/n)i=1n(Xi1)2,~22=(1/n)i=1n(Yi2)2, and ~=[i=1n(Xi1)(Yi2)/n~1~2] respectively, provided that n3.

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