Let X1, X2,...,X, be a set of independent random variables each following the distribution with pdf 1 f(r|0) = (1-0)/ª on 00. It can be shown that 1 02 E(X) E(log X) = -0 and V(X) = 1+0 (1+ 20)(1+0)²* It can also be shown that the MLE of 0 is 6, =-L log X; (a) According to the Central Limit Theorem, as given in Unit 1, what is the asymptotic distribution of X = (E X;)/n? State its parameter(s). (b) Show that d 1 2 log r. 02 03 (c) Show that the Fisher information based on a single observation for 0 is 1 i(0): 02 (d) Use the result stated in part (c) to give the asymptotic distribution of On-

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