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(b) Show that log r. 02 (c) Show that the Fisher information based on a single observation for 0 is 1 i(4): 02 (d) Use the result stated in part (c) to give the asymptotic distribution of 0n.

(b) Show that log r. 02 (c) Show that the Fisher information based on a single observation for 0 is 1 i(4): 02 (d) Use the result stated in part (c) to give the asymptotic distribution of 0n.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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Do just part b,c,d

Let X1, X2,..., X, be a set of independent random variables each following the distribution with pdf 1 z(1–8)/ on 0 < r < 1, with 0 > 0. It can be shown that 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 -E÷, log X¡ (a) According to the Central Limit Theorem, as given in Unit 1, what is the asymptotic distribution of X, = (E1 X;)/n? State its parameter(s). (b) Show that 1 2 02 log r. (c) Show that the Fisher information based on a single observation for 0 is 1 i(0) (d) Use the result stated in part (c) to give the asymptotic distribution of On.
Transcribed Image Text:Let X1, X2,..., X, be a set of independent random variables each following the distribution with pdf 1 z(1–8)/ on 0 < r < 1, with 0 > 0. It can be shown that 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 -E÷, log X¡ (a) According to the Central Limit Theorem, as given in Unit 1, what is the asymptotic distribution of X, = (E1 X;)/n? State its parameter(s). (b) Show that 1 2 02 log r. (c) Show that the Fisher information based on a single observation for 0 is 1 i(0) (d) Use the result stated in part (c) to give the asymptotic distribution of On.
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