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3. Let X₁,..., X₁, be iid random variables following density function aba xa+I, f(x; a) = x> b, with the unknown parameter a > 2 and known b>0. Its expectation and variance follow E(X) = ab/(a− 1) and Var(X) = b²a/{(a − 1)² (a − 2)}. (a) Show that the MLE of a equals âMLE = n/₁ log(X;/b). (b) Calculate the asymptotic variance of âMLE. (d) Find the MLE of EX. (c) Find the 100(1 – a) % asymptotic confidence interval of a. (e) Find the Cramér-Rao lower bound for EX

3. Let X₁,..., X₁, be iid random variables following density function aba xa+I, f(x; a) = x> b, with the unknown parameter a > 2 and known b>0. Its expectation and variance follow E(X) = ab/(a− 1) and Var(X) = b²a/{(a − 1)² (a − 2)}. (a) Show that the MLE of a equals âMLE = n/₁ log(X;/b). (b) Calculate the asymptotic variance of âMLE. (d) Find the MLE of EX. (c) Find the 100(1 – a) % asymptotic confidence interval of a. (e) Find the Cramér-Rao lower bound for EX

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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Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!Please do not rely too much on chatgpt, because its answer may be wrong. Please consider it carefully and give your own answer. You can borrow ideas from gpt, but please do not believe its answer.Very very grateful!

3. Let X₁,..., X, be iid random variables following density function aba xa+Ī, f(x; a) = = x>b, with the unknown parameter a > 2 and known b > 0. Its expectation and variance follow E(X) = ab/(a− 1) and Var (X) = b²a/{(a − 1)² (a − 2)}. (a) Show that the MLE of a equals âMLE = n/₁ log(X;/b). (b) Calculate the asymptotic variance of âMLE. (d) Find the MLE of EX. (c) Find the 100(1 − a)% asymptotic confidence interval of a. (e) Find the Cramér-Rao lower bound for EX
Transcribed Image Text:3. Let X₁,..., X, be iid random variables following density function aba xa+Ī, f(x; a) = = x>b, with the unknown parameter a > 2 and known b > 0. Its expectation and variance follow E(X) = ab/(a− 1) and Var (X) = b²a/{(a − 1)² (a − 2)}. (a) Show that the MLE of a equals âMLE = n/₁ log(X;/b). (b) Calculate the asymptotic variance of âMLE. (d) Find the MLE of EX. (c) Find the 100(1 − a)% asymptotic confidence interval of a. (e) Find the Cramér-Rao lower bound for EX
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