Question: 7. Suppose the random variables Y_1, Y_2, ..., Y_n satisfy Y_i = x_i + i , i = 1, 2, ..., n where x1, x2,

7. Suppose the random variables

Y_1, Y_2, ..., Y_n satisfy Y_i = x_i + i , i = 1, 2, ..., n

where x1, x2, ..., xn are fixed constants and 1, 2, ..., n are iid N(0, ^2 ), ^ 2 unknown.

(a) Find Find the MLE of and show that is an unbiased estimator of . (

b) Find the distribution of the MLE of

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