5 Suppose that X1, , Xn are normal with mean 1 Y1, , Yn are normal with mean 2 and W1, ,Wn are normal with mean 1 2 Assuming that all 3n random variables are independent with a common variance, find the maximum likelihood estimators of 1 and 2 ...

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5. Suppose that X1, . . . , Xn are normal with mean 1; Y1, . ....

Question:

5. Suppose that X1, . . . , Xn are normal with mean μ1; Y1, . . . , Yn are normal with mean μ2; and W1, . . . ,Wn are normal with mean μ1 + μ2. Assuming that all 3n random variables are independent with a common variance, find the maximum likelihood estimators of μ1 and μ2.

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