I. Based on a random sample of 3 observations, consider two competing estimators of the population mean µ: (X1+ X2 + X3), î2 = 1 X1+-X2+÷X3 %3D (a) Are they unbiased? (b) Which estimator is more efficient? How much more efficient? 2. Let {X1, X2, . .., X„} be an independent random sample from Poisson(^), (a) Show that both X and S² are unbiased estimator of ). (b) Calculate the Cramer-Rao Lower Bound with respective to A. (6) Which estimator should be preferred and uvby?
I. Based on a random sample of 3 observations, consider two competing estimators of the population mean µ: (X1+ X2 + X3), î2 = 1 X1+-X2+÷X3 %3D (a) Are they unbiased? (b) Which estimator is more efficient? How much more efficient? 2. Let {X1, X2, . .., X„} be an independent random sample from Poisson(^), (a) Show that both X and S² are unbiased estimator of ). (b) Calculate the Cramer-Rao Lower Bound with respective to A. (6) Which estimator should be preferred and uvby?
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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q2b and q2c
![1. Based on a random sample of 3 observations, consider two competing estimators of the population
mean u:
în =(X1 + X2 + Xa), ia = ;X1 +x2 + X3
4
(a) Are they unbiased?
(b) Which estimator is more efficient? How much more efficient?
2. Let {X1, X2, ..., Xm} be an independent random sample from Poisson(A),
(a) Show that both X and S² are unbiased estimator of ).
(b) Calculate the Cramer-Rao Lower Bound with respective to A.
(c) Which estimator should be preferred and why?](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F18f8660f-48dc-4e5a-972e-f0de82ccda7c%2F0116492b-28c0-409d-9341-3f918c289e0b%2Flj7kw2b_processed.png&w=3840&q=75)
Transcribed Image Text:1. Based on a random sample of 3 observations, consider two competing estimators of the population
mean u:
în =(X1 + X2 + Xa), ia = ;X1 +x2 + X3
4
(a) Are they unbiased?
(b) Which estimator is more efficient? How much more efficient?
2. Let {X1, X2, ..., Xm} be an independent random sample from Poisson(A),
(a) Show that both X and S² are unbiased estimator of ).
(b) Calculate the Cramer-Rao Lower Bound with respective to A.
(c) Which estimator should be preferred and why?
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