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You have a random sample with n iid observations from the following density: Le- if x >0 f(x) = otherwise where the parameter r > 0. For this distribution, we have: 4 – T E[X]: var[X] = 2 (a) Show that the maximum likelihood estimator of r is: n 1 ÎMLE 2n i=1 (b) Is îMLE an unbiased estimator for r? Justify your answer. (c) Find the Fisher information and construct a large-sample 95% confidence interval for r.

You have a random sample with n iid observations from the following density: Le- if x >0 f(x) = otherwise where the parameter r > 0. For this distribution, we have: 4 – T E[X]: var[X] = 2 (a) Show that the maximum likelihood estimator of r is: n 1 ÎMLE 2n i=1 (b) Is îMLE an unbiased estimator for r? Justify your answer. (c) Find the Fisher information and construct a large-sample 95% confidence interval for r.

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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(d) Find the method of moments estimator of r. Is it a consistent estimator for r? Justify your answer.
Transcribed Image Text:(d) Find the method of moments estimator of r. Is it a consistent estimator for r? Justify your answer.
You have a random sample with n iid observations from the following density: if x > 0 2r f(x) = otherwise where the parameter r > 0. For this distribution, we have: 4 varįX] = ",", Tr E[X] 2 2 (a) Show that the maximum likelihood estimator of r is: n 1 TMLE = 2n i=1 ΣΧ (b) Is rMLE an unbiased estimator for r? Justify your answer. (c) Find the Fisher information and construct a large-sample 95% confidence interval for r.
Transcribed Image Text:You have a random sample with n iid observations from the following density: if x > 0 2r f(x) = otherwise where the parameter r > 0. For this distribution, we have: 4 varįX] = ",", Tr E[X] 2 2 (a) Show that the maximum likelihood estimator of r is: n 1 TMLE = 2n i=1 ΣΧ (b) Is rMLE an unbiased estimator for r? Justify your answer. (c) Find the Fisher information and construct a large-sample 95% confidence interval for r.
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