I would like to know the answer to Q6 i) . I can find a sufficient statistic using exponential family sufficient statistic property, but I don't know whether it proves to be complete. I would like to find a statistic that is complete and sufficient.

Q6. Let X1, X2, - - - Xn be an independent random sample from NUS', (92) with 6 7E 0. (i) Find a complete and sufcient statistic of (9; (5 marks) (ii) Derive the maximum likelihood estimator of 9; (5 marks) (iii) Derive the asymptotic distribution of the estimator found in part (ii). (5 marks) 12:36 AM Thu Apr 1 61% Q ND STAT2602 ASSIGNMENT 2 ~ + X ... 3 . Feb ... X Tutorial 5 X cpart2 X 40dbe2b4be 3d57... X STAT2602 ASS... X Assign 2 [0] T . Q6. Let X1, X2, . . . Xn be an independent random sample from N(0, 02) with 0 # 0. i) Find a complete and sufficient statistic of 0; (5 marks) (ii) Derive the maximum likelihood estimator of 0; (5 marks) iii) Derive the asymptotic distribution of the estimator found in part (ii). (5 marks) i ) X. ~ N ( D, 0 ' ) Since the distribution of X is part of exponential family to find sufficient statistic from p. d.f f ( (;0 ) f ( x x ; 0 ) = h ( > ( ) c ( 0 ) exp f * p ; co ) t : ( 0 ) } f ( x ; 0 ) = no expf - * ( * * " ) ? Dax exp { - x -2x0 to* ? Van * 0 Xe = exp { -