Assume X1,X2, ., Xn are random samples from X~Exponential(0). .... 1) Find the MLE estimator of 0. 2) Find Cramer Rao lower bound for this estimator and analyze the efficiency. More precisely, you have to find the variance of the estimator using conventional methods and compare it to the Cramer Rao lower bound; 3) Assume that we have taken a random sample from such a distribution and the sample

Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter2: Exponential, Logarithmic, And Trigonometric Functions
Section2.CR: Chapter 2 Review
Problem 111CR: Respiratory Rate Researchers have found that the 95 th percentile the value at which 95% of the data...
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My data sets were given picture which I sent in front of my name

('Bashir', 'Hatamov')
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Transcribed Image Text:('Bashir', 'Hatamov') [65747668 4 267 623 4674 664 6648 5 64 6]
Question 3
Assume X1, X2, ... , Xn are random samples from X~Exponential(0).
п
1) Find the MLE estimator of 0.
2) Find Cramer Rao lower bound for this estimator and analyze the efficiency. More
precisely, you have to find the variance of the estimator using conventional methods and
compare it to the Cramer Rao lower bound;
3) Assume that we have taken a random sample from such a distribution and the sample
mean X equals to the sum of the squares of the first 5 values in your dataset. Apply the
delta method to obtain the asymptotic distribution of X2.
Transcribed Image Text:Question 3 Assume X1, X2, ... , Xn are random samples from X~Exponential(0). п 1) Find the MLE estimator of 0. 2) Find Cramer Rao lower bound for this estimator and analyze the efficiency. More precisely, you have to find the variance of the estimator using conventional methods and compare it to the Cramer Rao lower bound; 3) Assume that we have taken a random sample from such a distribution and the sample mean X equals to the sum of the squares of the first 5 values in your dataset. Apply the delta method to obtain the asymptotic distribution of X2.
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