Q-1 (7+10+5)( a) Let XiN(1,2),i=1,,m, iid, and YjN(2,22),j=1,,n, iid, be two independent random samples with all parameters unknown. Find a complete sufficicut statistic of =(1,2,2). Compute UMVUEs of (12)2 and of 2. (b) In (a), let 1=2=. Find MLE, , of the vector =(,2). Compute Fisher information matrix and variance-covariance matrix of . (c) For (b), check if E[S()]=0 and E[H()]=Var[S()], where S() denotes the score function and H() is the Hessian. (You can assume any regularity condition if needed.)