statistics

Question 4 Suppose that for a promss XL, Vor[X] : 0'2, but Mt) : or + t where t > {I and or, ,3 are imknotvn constants. Assume that a BS of size n can be obtained independently at an);r particular t and let X! denote the sample mean estimator at time t Let {t1, t2, .. . , tk } denote the (distinct) time points at which independent 113's are to be obtained, and consider the estimator p? where the refs are constants. B 2 wife + weft: + * * ' + \"Hafiz; a Show that the w,- ean be solved ex licitl when It : 2 and [i is an HE P Y (b) To solve for the as; when I: 2: 2, requires that an additional criterion be used. A natural criteria is that It? should have the smallest possible variance. {See LM notes) (i) Construct the Lagrangian and derive the i'th partial derivative equation. {ii} Hence show that A1 : A2t_, where t denotes the sample average of t1. t2,. . . , 13;; (t.- fl 2:21 (i:- t )2 [iii] Thus show that m