Q6. Suppose that X =61 + 52, where 1 N N(6,1), 52 ~ N()\\6', A2), and 1 and 52 are in- dependent. Here, A 2 1 is a given constant, and 6 is a unknown parameter. (iv) Let X 1, X 2, - - - ,Xn be an independent random sample from the distribution of X. Find the MLE of a (denoted by 791). (v) Will a} be the UMVUE of 6 and why? A 1 n 1 3' (vi) Let 62 = Z Xi be another estimator of 9. Calculate the mean squared error 1 -|- A i=1 2 of El} . (vii) Will 9; be better than 31 in terms of mean squared error and why